The centre half, who was on loan at Tranmere earlier in the season, will be on loan at Shrewsbury for a month.
Speaking to Shrewsbury's official club website, Graham Turner said:
"We've taken 20 year old Jermaine Grandison on an initial month's loan from Coventry City.
"Jermaine's recently been on loan at Tranmere Rovers and did well there and he is a player we want to take a good look at.
"He's a player I've seen a few times and had watched and is one where the loan deal could possibly turn into a permanent one.
"We want to look at him but more importantly he wants to come to train with us and take a good look at Shrewsbury Town."
Picture copyright of Covsupport News Service. Credit CNS/SB
"We want to look at him but more importantly he wants to come to train with us and take a good look at Shrewsbury Town."
Picture copyright of Covsupport News Service. Credit CNS/SB