Is it possible to write a validation rule which will fire only on insert of record not on update of record in salesforce ?

Hi saurabh,

You can check the record is new or existing one using ISNEW() function in formula.

Ex:
IF( !ISNEW() , Your validation logic, false);
or
AND(! ISNEW() ,Your validation logic)

Please let me know, if it helps you.

Best Regards,
Manpreet.