I m trying to connect a parallel LCD with microcontroller serial port via serial to parallel converter.
LCD shows random cursor blinking on different points
An important issue is that a serial-to-parallel converter is intended for sending data to a parallel printer.
But such an adapter does not automagically allow a program to control all signals on the Centronics interface.
Does your adapter support full control of the handshake signals? Or do your display behaves identical to a parallel printer when it comes to strobing of data etc?
I think that's rather a large assumption!
In the absence of any other information, a "serial to parallel converter" could be anything that converts from any serial interface to any parallele interface.
The fact that the OP didn't think to give any further detail does suggest a high likelihood that, whatever it is, it isn't suitable for this task...