In this paper, an efficient implementation of the multiple-model generalized labeled multi-Bernoulli filter (MM-GLMB) is presented for tracking multiple maneuvering targets. To alleviate the generation of the redundant components, the original two-staged implementations of MM-GLMB filter are integrated into a single step bringing the benefit that only one truncation procedure is required per iteration. In this study, the authors take the convergence behavior of the Gibbs sampling into full consideration to improve the convergence rate. The blocked Gibbs sampling over lattice Gaussian distribution based solution to the implementation of MM-GLMB filter is proposed to greatly relax the computational load. The numerical simulations demonstrate the efficacy of the proposed algorithm with low computational cost.