This paper proposes a vector modulation-based model predictive current control strategy for a two-stage matrix converter. The switching frequency is kept constant by fixing the switching instantly. The control scheme controls the source reactive power on the input side and output currents on the output side. Besides, 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, to ensure zero-current switching operations and reduce the switching losses, an optimal switching sequence is proposed and implemented. Furthermore, considering that the input filter resonance is easier to be inspired by the model predictive control, compared with conventional linear control strategies, an innovative active damping technique is proposed to suppress the input filter resonance. To assess the performance of the proposed method, simulation and experimental results are demonstrated, showing that the control system features both good steady-state and transient performance.