If you have Mozilla Firefox then FireFTP is a free, secure, cross-platform powerful FTP client extension.

# First of all, you need Firefox to run FireFTP. FireFTP is an extension to the Firefox browser.
# To install FireFTP, go to http://fireftp.mozdev.org and click on the ‘Download FireFTP’ link on the main page.

Note: If you want browser-based FTP client(Internet Explore, Firefox), then Anyclient is the solution which can be run from any computer with Java installed.

Anyclient is a browser-based FTP client that can be run from any computer with Java installed. Unlike FireFTP, which is a browser add-on that you need to install before running, you can fire up AnyClient just by visiting a web site.

AnyClient is a free platform independent file transfer application that supports all major file transfer protocols including FTP/S, SFTP and WebDAV/S.

Visit AnyClient here