It will be very difficult to close your credit card without affecting your CIBIL score. But what you can do is that you close it and make the next bill payments on time. It will give a boost to your CIBIL scores. Might be a good option, planning it is very important
It will surely affect your score
If very new account and you have multiple old accounts it will affect less.
And if it's old account it will affect more
Your credit age won't just drop by closing the old card.
TransUnion will be having the credit in there showing it as "Closed card."
All the dates of that card, including timely bill payments will be shown.
I closed 3 of my oldest cards and it did not affect my credit age or score.
My father took a personal loan in 2009 and now his credit age is 15years.
Now his oldest credit is from SBI 9years even if he closes it his credit age will still be 15years, it has no effect on score.
I recommend you take 1year subscription of CIBIL and observe how cibil score works.