This paper presents a collision avoidance scheme for wireless sensor networks that use a GTS-based channel allocation scheme. Many sensor nodes can share a GTS channel for sending their data to the sink node. When a node tries to send a frame at a shared GTS channel, a collision can be occurred when there is a node that uses the same backoff number. For decreasing a wireless collision, the parent assigns a backoff number when a child node registers to it. Further, when a collision occurs during a data transfer, the parent node reassigns a new backoff number for the child node. Simulation results show that there is a decreased collision number with suggested parent-controlled collision avoidance scheme by effectively controlling the backoff number of the child.