The boy was badly injured when a car overturned in Farnley on Friday evening.
He was a passenger in a blue Subaru Impreza that veered off Tong Road and hit a wall and a lamppost before ending up on its roof just before 5pm.
Police said the boy was one of two people in the Subaru who were injured in the crash, which happened near the Beulah pub.
The boy was taken to Leeds General Infirmary, where he was at first said to be in a critical condition.
This morning, police said he was now stable and his injuries were no longer believed to be life-threatening.
Police would like to speak to anyone who saw the Subaru before the collision or anyone who witnessed the collision itself who they have not already spoken to. Call the Eastern Area Roads Policing Unit via 101, quoting log 1289 of 30/11.