Does arduino support parallel communication? is there any specific package available that can do this?
Well it could certainly be programmed to emulate any TTL level parallel protocol up to it's number of 20 I/O pins available. Perhaps you could be more specific on what you are requiring.
Lefty
If you mean parallel as in a parallel printer interface, then the proper name is a Centronic parallel interface. It uses eight pins, plus a few handshaking lines. And yes, the Arduino can do that, with suitable programming. It'll use up quite a few of the I/O pins, of course.