With the development of power switches and processor performance in recent years, the control frequency of inverters has been significantly improved. However, limited by technology and price, the sensor sampling frequency in large-scale industrial applications is much lower than the inverter control frequency that can be realized. This frequency mismatch limits the performance improvement of the inverter. In this article, the current and voltage at the non-sampling time are reconstructed using the current prediction control principle and the input observer theory, allowing a single-phase inverter to implement multi-sampling rate control with a low sampling frequency and high control frequency. In addition, an improved adaptive controller is designed to solve the effect of incorrect model parameters, which realizes adaptive control when the sampling frequency and control frequency are mismatched. Finally, the effectiveness of the method is verified through a simulation and experiments. The proposed method can solve the problem of high-speed switching for inverters under low-sampling-frequency conditions, improving the inverter’s adaptive performance and robustness.