Power converters under the model predictive control (MPC) inherently suffer from nonignorable steady-state residuals in its control outputs when it exists a mismatch in the parameters between the actual system in control and the system's model adopted in the control. In this brief, an adaptive reference MPC (ARMPC) is proposed in response to this issue. Unlike those conventional derivatives of MPC, the ARMPC is designed to track the so-called virtual references instead of the actual references. The virtual references are generated by a flexibly modeled virtual multiple input multiple output system. Consequently, additional tuning is not required for different operating conditions. ARMPC has been applied to a single-phase full-bridge voltage-source inverter with both resistive and resistive-inductive loads. It is experimentally verified that the proposed ARMPC can significantly attenuate the steady-state offsets in the environment of model mismatch (which is an inherent problem of MPC without significantly sacrifice transient performance). Also, a demonstration that ARMPC renders a consistent attenuation of steady-state errors than the conventional MPC with integrator is provided. More importantly, ARMPC shows better transient performance than the MPC with integrator for some cases.