This paper proposes a low-complexity model predictive control (L-MPC) method for a five-leg inverter (FLI) that independently drives dual three-phase induction motors (IMs). In the FLI system, a conventional MPC method considers all 32 candidate voltage vectors. This method causes a high computational burden and may limit the control period in the controller with low performance. However, low computation can be achieved using the L-MPC method considering only 4 candidate voltage vectors. In the L-MPC method, two IMs are prioritized, and the priority of both IMs alternates every control period. High-priority motor selects the voltage vector with the lowest cost among 3 effective vectors and 1 zero vector based on the sector where the reference voltage vector is located. Low-priority motor is automatically determined based on the previously selected voltage vector from high-priority motor. L-MPC method considers fewer candidate voltage vectors than the conventional method and results in the high switching frequency by reducing the computation time, which results in reduction of current THD. The validity of the proposed method is verified by simulations and experimental results.