The modular multilevel matrix converter (M3C) is the core component in low-frequency AC (LFAC) transmission, which is a competitive scheme for offshore wind power integration. In this paper, the M3C control strategy with the reduced switching frequency SM voltage balancing method is proposed. First, based on the conventional αβ0 and dq transformations, the M3C mathematical model is derived. Then, the dual-loop control structure with outer loop and inner loop controllers commonly used in voltage source converters is applied to the M3C. The inner loop controller consists of the current tracking controller in the dq reference frame and the circulating current suppressing controller in the αβ0 reference frame; the outer loop controller is proposed for the offshore wind farm LFAC integration scenario. Additionally, according to the operating characteristics of full-bridge sub-modules (FBSMs), three characteristic variables are defined and a reduced switching frequency SM voltage balancing method based on the nearest level control (NLC) is proposed. Finally, time-domain simulations in PSCAD/EMTDC demonstrate the feasibility of the proposed control strategy.