I almost know that it's due to data on TxD and RxD pins, which are shared by the RS and RW lines of LCD. How do I eliminate it?

By not using these pins for other purposes than serial I/O it is an ALTERNATE function, not a DUAL function.

I am quite a novice working with microcontrollers

Read the three 80C51_FAM_*.pdf documents. found at
http://www.semiconductors.philips.com/products/...other.html

Have fun,

Erik