Getting wrong result from JSON - Python 3

It does so because there is no publisher entry in volumeInfo of the first entry, thus it raises a KeyError and your except captures it. If you're going to work with fuzzy data you have to account for the fact that it will not always have the expected structure. For simple cases you can rely on dict.get() and its default argument to return a 'valid' default entry if an entry is missing.

Also, there are a few conceptual problems with your function - it relies on a global gr which is bad design, it shadows the built-in dict type and it captures all exceptions guaranteeing that you cannot exit your code even with a SIGINT... I'd suggest you to convert it to something a bit more sane:

def book_search(search_term, max_results=3):
    results = []  # a list to store the results
    parms = {"q": search_term, "maxResults": max_results}
    r = requests.get(url="https://www.googleapis.com/books/v1/volumes", params=parms)
    try:  # just in case the server doesn't return valid JSON
        for result in r.json().get("items", []):
            if "volumeInfo" not in result:  # invalid entry - missing volumeInfo
                continue
            result_dict = {}  # a dictionary to store our discovered fields
            result = result["volumeInfo"]  # all the data we're interested is in volumeInfo
            isbns = result.get("industryIdentifiers", None)  # capture ISBNs
            if isinstance(isbns, list) and isbns:
                for i, t in enumerate(("isbn10", "isbn13")):
                    if len(isbns) > i and isinstance(isbns[i], dict):
                        result_dict[t] = isbns[i].get("identifier", None)
            result_dict["title"] = result.get("title", None)
            authors = result.get("authors", None)  # capture authors
            if isinstance(authors, list) and len(authors) > 2:  # you're slicing from 2
                result_dict["author"] = str(authors[2:-2])
            result_dict["publisher"] = result.get("publisher", None)
            result_dict["published_date"] = result.get("publishedDate", None)
            result_dict["description"] = result.get("description", None)
            result_dict["pages"] = result.get("pageCount", None)
            genres = result.get("authors", None)  # capture genres
            if isinstance(genres, list) and len(genres) > 2:  # since you're slicing from 2
                result_dict["genre"] = str(genres[2:-2])
            result_dict["language"] = result.get("language", None)
            result_dict["image_link"] = result.get("imageLinks", {}).get("thumbnail", None)
            # make sure Google_Results accepts keyword arguments like title, author...
            # and make them optional as they might not be in the returned result
            gr = Google_Results(**result_dict)
            results.append(gr)  # add it to the results list
    except ValueError:
        return None  # invalid response returned, you may raise an error instead
    return results  # return the results

Then you can easily retrieve as much info as possible for a term:

gr = book_search("Google")

And it will be far more tolerant of data omissions, provided that your Google_Results type makes most of the entries optional.