This paper studies the optimal control problem for discrete-time switched linear systems with quadratic cost. A model predictive control (MPC) scheme is proposed which results in closed-loop strategies for both switching and control inputs. To reduce the online computation and ensure stability of the MPC scheme, a two-stage pruning algorithm is constructed which is performed offline. The resulting MPC scheme ensures exponential stability, and the cost function is suboptimal. Stability, feasibility, and suboptimality of the MPC scheme are studied. Simulation results are given for the MPC scheme which shows the proposed approach results in reduced computation and acceptable performance.