Nextion Display and Arduino Due Processing Problem

I have an issue while interfacing Nextion HMI with Arduino (Due) regarding its processing speed.
If controller is busy in writing data on HMI, so it missed the task which it has to performed in parallel.
Can someone help me in this regard

Hello Husnain,
Welcome to the forum.

Please read 'how to use this forum - please read', especially item #7 about posting code. You are asking us for help with code we cannot see; while there are some very clever people here I doubt any of them are telepathic.

Are you:
Using my methods as set out in the tutorial 'using nextion displays with Arduino'? My methods put very little demand on the host Arduino and would not, I think cause a problem.

Using the Nextion libraries as supplied by Nextion? If so, be aware they are full of bugs. Ray Livingston has re-written the libraries and removed many of the bugs. There is a link to Ray's version of the libraries from my tutorial, so you can download them if you wish.

Or maybe you have devised your own method of communicating with a Nextion, in which case I cannot comment without seeing what you are doing.