A computational efficient multiobjective model predictive control (MO-MPC) scheme with prioritized objectives is proposed for linear time-invariant system with state and input constraints. The terminal states are decomposed into several auxiliary decision variables and then the traditional terminal control law is parameterized by using the several corresponding controller gains. According to the priorities of multiple objectives, the MO-MPC problem is reformulated as a multi-layer single objective one. Moreover, by establishing the conditions on the most important objective, the recursive feasibility and asymptotic stability properties of the designed MO-MPC are proved by the method of the triplet of the terminal constraints, terminal penalty functions and local state feedback laws. Finally, the advantages of the new MO-MPC are illustrated by a numerical example in terms of the enlargement of terminal set and the low computation loads.