Model predictive control (MPC) is an outstanding control method which can achieve superior dynamic response, nonlinear control and multi-objective collaborative control. However, because of unfixed switching frequency, the harmonic spectrum of the output current is dispersed, which would make it difficult to design the output filter. In this work, a double voltage vector model predictive control (DVV-MPC) algorithm for grid-connected cascade H-bridge (CHB) multilevel inverter is presented. The algorithm not only has the advantages of MPC but also produces fixed the switching frequency of the inverter. It is realized by a modulation stage with two adjacent voltage vectors in one switching cycle. And the duty cycle of the associated voltage level is obtained by minimizing an additional cost function. This method is suitable for the cascades of n cells inverter. For reducing the computation burden and eliminating the computation delay, adjacent regions prediction method and time-delay compensation method are applied to the inverter. Finally, in this paper, the proposed strategy is applied to a single-phase grid-connected 7-level CHB inverter. Simulation and experiment are executed to show the advantages of the proposed control algorithm in dynamic state and steady state.