The WiMAX multicast and broadcast polling modes uses the Truncated Binary Exponential Backoff (TBEB) algorithm as the Contention Resolution Process among distributed mobile nodes while the network traffic load is nearly saturation. TBEB suffers from high collision probability under a high traffic load. TBEB thus significantly degrades the grade of service, especially while considering handoff in the mobile WiMAX network. Thus, this work first proposes an efficient contention resolution algorithm that consists of two key contributions: 1) providing the adaptive minimum-maximum backoff values algorithm (AM 2 ) to partition collision domains and 2) supporting a dynamic waiting-penalty algorithm (DWP) for successful contentions to dynamically decrease CWs while contentions randomly selecting the same CW. Second, we model the proposed approach as a discrete-time Markov chain model, and then mathematically analyze important metrics: collision probability and throughput. Numerical results indicate that the analytical results are very close to the simulation results, which justify the accuracy of the analytical model. Additionally, the proposed algorithm outperforms IEEE 802.16 and all compared approaches in collision probability and network throughput.