Single-phase H-bridge converter has the advantages, such as lower power device voltage stress, fewer passive components, and variable output voltage polarity. Single-phase Hbridge converter has been applied in many applications with a wide input voltage range, and it has strong demand background and the value of promotion and application. Predictive current control (PCC) of a single-phase H-bridge converter has the fastest dynamic response when tracking the reference current, but the control delay will cause a steady-state error in the inductor current. To better control the inductor current of a single-phase H-bridge converter, this paper proposes to use the mathematical model of the converter to minimize the error of the predicted current and the reference current, so that the converter has a faster response speed and a smaller current overshoot, the stability of the single-phase H-bridge converter is guaranteed. At the same time, a state observer is proposed to improve the estimation of the inductor current in control delay compensation. The research results show that PCC has a good control effect in a single-phase H-bridge converter.