This paper presents energy-function based model predictive control (EF-MPC) for single-phase split source inverters. Unlike conventional model predictive control (MPC) methods, the proposed EF-MPC is designed by considering the stability of inverter. According to the Lyapunov's direct method, the stability of inverter can be assured if the derivative of energy-function is always negative. Motivated from this fact, the design of cost function in EF-MPC is based on the energy function which involves dc- and ac-side inductor current errors. It is shown that the coefficient used in the formulation of energy function is redundant which eliminates the weighting factor required in the multi-objective cost function. Elimination of the weighting factor not only simplifies the controller design in the practical implementation, but also removes the weighting factor tuning process needed in the conventional predictive methods. Another advantage of the proposed EF-MPC is that the amplitude of low-frequency component in the dc-side inductor current is suppressed. The steady-state and dynamic performances of the proposed EF-MPC are investigated experimentally under linear and nonlinear loads. In both cases, the dc-side variables are regulated at the desired values while the sinusoidal output voltage with low total harmonic distortion is obtained in the ac-side.