Bandwidth used by ftp user
 

Is there a way we can check bandwidth used by a ftp user.
I am using vsftpd on fedora machine.

ntop or iftop may show you traffic broken down by destination. (iftop is command line, ntop runs as a service and makes results available via a local web server)

Other things I would research (I don't actively use them myself):
iptraf
nethogs

both of them does not work on fedora.

My choice could be cacti .For Fedora you can use vnstat Console based network traffic monitor

Is there a built in tool through which we can know how much bandwidth a particular user is using. I am using fedora and running vsftpd on it.

I doubt very much there is a built-in tool. Also I would be very surprised if nethogs (and all of the others I mentioned) cannot be installed in Fedora. Have you tried?

nethogs fedora - Google Search leads me to Linux Toolkits: Monitoring net hogs using nethogs which says
And the same should apply to other suggestions - I'm not saying nethogs is the best.

Is there a reason why you can't install additional packages?