In view of the problems of large amount of calculation and low efficiency resulted by pruning of generalized labeled multi-Bernoulli(GLMB) prediction and updating steps, as well as deficiency of only taking single motion model into consideration, a model of multiple model one step updating GLMB maneuvering extended target tracking algorithm is proposed. Firstly, by merging prediction step with updating step through formula deduction, a new step recursion expression is proposed. Then, the multiple model algorithm is introduced to one step recursion expression to obtain the final step of update equation, and a quick pruning method is proposed based on Gibbs for sampling. Since the improved algorithm only involves one pruning and the pruning method is efficient, the operation time of the algorithm is greatly shortened. At the same time, the multiple model is used to improve the tracking accuracy of the maneuvering target. Simulation results show that the proposed algorithm can effectively estimate the state of the maneuvering target, and the computational efficiency is significantly improved compared to the MMGLMB filter.