Hi
All you need is grant permission for the procedure owner .
Because
"If the same user owns a stored procedure and all the views or tables it references, and if the procedure and objects are all in the same database, SQL Server checks only the permissions on the procedure".

This security mechanism also known as ownership chain.

"If the ownership chain of a procedure or view is broken (not all the objects in the chain are owned by the same user), SQL Server checks permissions on each object in the chain whose next lower link is owned by a different user. Only those statements where the user has the necessary permissions will be executed, and the remaining statements will get an "Insufficient Permissions" error. In this way, SQL Server allows the owner of the original data to retain control over its accessibility.
"

PS
Microsoft recommends to use dbo as owner of all database objects.