Using an array inside a constructor using Javascript

You have a couple things messed up. If you are going to pass the grades array in as an argument, then you need to set grades with this:

this.grades = grades;

Also in the average function you need to refer to grades with this.grades not just grades. This will allow you to add more grades later and still get the correct average. You could also consider making the grades optional by defining the constructor with something like:

function student(name, surname, number, grades =[])

Then if you don't pass in a value, an empty array will be waiting for you.

In the end you might have something like:

function student(name, surname, number, grades = []) {
  this.name = name;
  this.surname = surname;
  this.number = number;
  this.grades = grades;
  this.average = function() {
    return this.grades.reduce((a, c) => a + c, 0) / this.grades.length
  }
}

var student1 = new student("Peter", "Cat", 14444, [2, 3, 4]);
console.log("Average: ", student1.average())

// add another grade:
student1.grades.push(6)
console.log("New Average: ", student1.average() )

You can solve same problem by using ES6, in your code, you are initializing this.grade=[] with an empty array inside function so further processing of average will be done on empty array only. For good practice, function parameters should be assigned with a default value, so that if mistakenly we do not pass an array as an argument then the function parameter will use the default value. Attaching code snippet for easy understanding in ES6.

class std{
constructor(name, surname, number, grades = []) {
    this.name = name;
    this.surname = surname;
    this.number = number;
    this.grades = grades;
}  

average() {
  if(this.grades.length !== 0){
    return this.grades.reduce((previous, current) => previous + current, 0) / 
    this.grades.length
  } else { return "no grades mentioned"; }
 }
}

var student1 = new std("Peter", "Cat", 14444, [1, 3, 4]);
console.log("Average: ", student1.average());
//add new student
var student2 = new std("Prasanna", "Test", 14444);
console.log(student2); 

//student2.grades.push(7)
//console.log("New Average: ", student2.average() )

You're already passing grades into the student() function, so you don't need to pass it in to the student.average function (as the inner function will already have access to the outer function parameter). Because of this, you also don't need to set this.grades = [].

Also, sum + = grades[i] should be sum += grades[i].

Simply fixing this error, then omitting passing grades into the inner function will correctly show the average, as can be seen in the following:

function student(name, surname, number, grades) {
  this.name = name;
  this.surname = surname;
  this.number = number;
  this.average = function() {
    var sum = 0;
    for (var i = 0; i < grades.length; i++) {
      sum += grades[i];
    }
    var average = sum / grades.length;
    return average;
  }
}

var student1 = new student("Peter", "Cat", 14444, [2, 3, 4]);
console.log(student1.average());

Your initialization of the variable is an empty array.

this.grades = [];

Should be

this.grades = grades;

However, I recommend that you study some javascript ES6 / ECMAScript 2015 and use classes. https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Classes

class Student {
  constructor(grades) {
    //... Other code
    this.grades = grades;
  }
}

you can use this line :

function student(name, surname, number, grades){ }

instead of this:

function student(name, surname, number, grades = [ ]){ }

function student(name, surname, number, grades) {
  this.name = name;
  this.surname = surname;
  this.number = number;
  this.grades = grades;
  this.average = function() {
    return this.grades.reduce((a, c) => a + c, 0) / this.grades.length
  }
}

var student1 = new student("Peter", "Cat", 14444, [2, 3, 4]);
console.log("Average: ", student1.average())

// add another grade:
student1.grades.push(6)
console.log("New Average: ", student1.average() )

We can use the Object Method to store the Average value:

function Student(name, surname, number, grades = [])
{
    this.name = name;
    this.surname = surname;
    this.number = number;
    this.grades = grades;

    //Method to calculate the Average
    this.average = function()
    {
        if(this.grades.length !==0)
        {
            //Return the Average Calculation
            return this.grades.reduce((previous, current) => previous + current, 0) / this.grades.length
        }
        else
        {
            //This will return if grades not provided
            return "No Grades Mentioned"
        }
    }

}

//With Grades
var student1 = new Student("Srinivasan", "Raja", 1635, [22,43,67,89,90]);
console.log(student1, "Average: "+ student1.average());

//Without Grades
var student1 = new Student("Denny", "Lawrence", 1635);
console.log(student1, "Average: "+ student1.average());