Move blocking is an input parameterization scheme that fixes the decision variables over arbitrary time intervals, commonly referred to as blocks, and it is widely implemented in model predictive control (MPC) to reduce the computational load during on-line optimization. Since the blocking position acts as the search direction in the solution space, selection of the blocking structure has a significant effect on the optimality of moved blocked MPC. However, existing move blocked MPC schemes apply arbitrary time-invariant blocking structures without considering the optimality of the blocking structure due to the difficulty in deriving a proper time-varying blocking structure on-line. Thus, we propose a semi-explicit approach for move blocked MPC that solves a multiparametric program for the blocking position set off-line and a simplified on-line optimization problem. This approach allows for a proper time-varying blocking structure for the current state on-line. The proposed approach can efficiently improve the optimality performance of move blocked MPC with only a little additional computational cost for critical region search while guaranteeing the recursive feasibility and closed-loop stability. (c) 2020 Elsevier Ltd. All rights reserved.