This paper proposes a novel model predictive current control scheme for two-stage matrix converter. The switching frequency is kept constant by fixing the switching instant. The control strategy achieves to control source reactive power in the input side and output currents in the output side. In addition, the advantage of the proposed strategy compared with conventional model predictive control is firstly proved using the principle of vector synthesis and the law of sines in the vector distribution area. Moreover, a zero-current switching sequence is proposed and implemented to insure zero-current switching operations and reduce the switching losses. Furthermore, in order to suppress the input filter resonance, which is easier to be inspired by the model predictive control, compared with traditional control strategies, an innovative active damping technique is proposed and implemented. Finally, both simulation and experiment are implemented to verify the performance of the proposed strategy. The results demonstrate that the control system features both good steady and transient performance.