An adaptive reference model predictive control (ARMPC) approach is proposed as an alternative means of controlling power converters in response to the issue of steady-state residual errors presented in power converters under the conventional model predictive control (MPC). Differing from other methods of eliminating steady-state errors of MPC based control, such as MPC with integrator, the proposed ARMPC is designed to track the so-called virtual references instead of the actual references. Subsequently, additional tuning is not required for different operating conditions. In this paper, ARMPC is applied to a single-phase full-bridge voltage source inverter (VSI). It is experimentally validated that ARMPC exhibits strength in substantially eliminating the residual errors in environment of model mismatch, load change, and input voltage change, which would otherwise be present under MPC control. Moreover, it is experimentally demonstrated that the proposed ARMPC shows a consistent erasion of steady-state errors, while the MPC with integrator performs inconsistently for different cases of model mismatch after a fixed tuning of the weighting factor.