AC/AC converter, as the key part of power conversion, plays an important role in the unique power quality conditioner, electric locomotive traction technology and frequency variation power supply. The modular multilevel AC/AC converter (AC/AC-MMC) is a promising topology for direct AC/AC converting applications. Under the background, according to the relationship between the arm electrical quantities and the input and output of the single AC/AC-MMC, the equivalent current decomposition model of decoupled input circuit, output circuit and circulating current circuit is derived in this paper. The independent control of the three circuits is realized successfully. Then, the performance indexes evaluation function of the current model and capacitor voltage balance is established. And the model predictive control (MPC) method based on arm level traversing is proposed and utilized to realize the accurate current tracking of input current, output current and circulating current as well as the balance control of submodule (SM) capacitor voltages. The method selects the optimal arm level with the goal of the optimal performance indexes in the evaluation function. Based on the proposed MPC method, the optimized method of SM internal loss equalization control is proposed by equally distributing the switching states of the left and right arm of each SM, realizing the balanced distribution of SM internal loss, and improving the operation reliability. Finally, the PSIM simulation model is established to validate the feasibility and effectiveness of the proposed control method.