Wi-Fi devices operate following the 802.11 distributed coordination function in order to fairly use the channel that the devices share. However, the throughput performance of the Wi-Fi networks is known to be degraded due to packet collisions. So, we propose a novel multiple access protocol, called centralized random backoff (CRB) for collision-free Wi-Fi networks. In CRB, after a successful reception of a data frame from a station, the access point allocates a unique backoff state to the station by means of the ACK frame. We evaluate its performance by comparing to that of a deterministic backoff mechanism. Evaluation results show that CRB significantly improves the throughput performance by reducing collisions, and it allows a larger number of nodes to operate in a collision-free state without dynamic parameter adjustment.