"On summer holidays" is better, and better is "on summer vacation" or "during summer vacation," as Jonathan points out, since the Summer doesn't consist of holidays.

I’m going to visit my grandmother during Summer holiday.

Hi Soraya I would suggest the following. I'm going to visit my grandmother during the Summer holidays. It is better to use the full word "grandmother" instead of "grandma".

I would suggest "during the summer holidays" or "over the summer holidays." In the US, it would be better to say "during summer vacation."