Yes you can definitely block anyone from your Gmail account, here are the steps for blocking person from Gmail such as:-

1-      Login your email id and password

2-      In right hand side click on setting

3-      Under setting section click on filter and block address

4-      Now choose email id or particular person email for blocked

This process will help to blocked Gmail id of one person or more than one person in Gmail. In the case of failure of process simply connect with

Gmail customer service phone number as they will provide you best guidance.