The matrix converter (MC) is a promising converter that performs the direct AC-to-AC conversion. Model predictive control (MPC) is a simple and powerful tool for power electronic converters, including the MC. However, weighting factor design and heavy computational burden impose significant challenges for this control strategy. This paper investigates the generalized sequential MPC (SMPC) for a three-phase direct MC. In this control strategy, each control objective has an individual cost function and these cost functions are evaluated sequentially based on priority. The complex weighting factor design process is not required. Compared with the standard MPC, the computation burden is reduced because only the pre-selected switch states are evaluated in the second and subsequent sequential cost functions. In addition, the prediction model computation for the following cost functions is also reduced. Specifying the priority for control objectives can be achieved. A comparative study with traditional MPC is carried out both in simulation and an experiment. Comparable control performance to the traditional MPC is achieved. This controller is suitable for the MC because of the reduced computational burden. Simulation and experimental results verify the effectiveness of the proposed strategy.