Inverters are commonly controlled to generate AC current and Total Harmonic Distortion (THD) is the core index in judging the control effect. In this paper, a THD oriented Finite Control Set Model Predictive Control (FCS MPC) scheme is proposed for the single-phase inverter, where a optimization problem is solved to obtain the switching law for realization. Different from the traditional cost function, which focuses on the instantaneous deviation of amplitude between predictive current and its reference, we redesign a cost function that is the linear combination of the current fundamental tracking error, instantaneous THD value and DC component in one fundamental cycle (for 50 Hz, it is 0.02 s). Iterative method is developed for rapid calculation of this cost function. By choosing a switching state from a FCS to minimize the cost function, a FCS MPC is finally constructed. Simulation results in Matlab/Simulink and experimental results on rapid control prototype platform show the effect of this method. Analyses illustrate that, by choosing suitable weight of the cost function, the performance of this THD oriented FCS MPC method is better than the traditional one.