Python: Zip files by extension type

I'm trying to zip all of the csv files in the current working directory to a new zipped folder at the end of my program. The folder is created in the right place, but when I open it, there's nothing inside. Here is my code:

# zip csv files into new folder
newzip = zipfile.ZipFile(os.path.join(os.getcwd(), "file.zip"), 'w')

for filename in os.getcwd():

    for name in filename:
        if filename.endswith('.csv'):
            newzip.write(proj)

I'm sure I'm missing something right in front of my face, so any help is appreciated!