Three-phase inverters with an output LC filter are commonly used to provide sinusoidal voltages with low-harmonic distortion. Constraint on peak filter current is often desirable to protect the components from potential damage. In case of constraints, implicit and explicit model-predictive control (MPC) are some of the feasible controller options. The conventional implicit MPC requires a large number of computations, whereas explicit MPC cannot directly incorporate real-time changes in model parameters, while still being computationally expensive than some of the other control schemes, e.g., hysteresis, dead beat control, etc. In this paper, we propose a new approach to solve the optimization problem in implicit MPC that has a computational complexity approximately five times less than that of explicit MPC. We have been able to achieve lower computational requirements by exploiting the inverter model and the structure of constraints.