Oliver is Baby Bear's baby cousin, whom Baby Bear meets in Episode 3709. Oliver communicates in baby talk, and travels around in a baby carriage. Oliver's favorite toy is his "wee little teddy person", and his favorite game is to bite Telly's nose. Oliver eats Grrr-Bear baby food; Baby Bear feeds him strained porridge. Oliver isn't afraid of big dogs, but he's afraid of triangles.

In episode 3816, Baby Bear resents having to take care of Oliver for the day. He likes being the baby in the family, and doesn't like having a younger cousin around to get all the attention. Telly encourages Baby Bear to recognize that taking care of a little cousin is an important responsibility.

When Oliver wants more food, Baby Bear imitates him by saying, "Please, sir, I want some more!" -- a reference to the Charles Dickens novel Oliver Twist.