Conventional buck power factor correction(PFC) converter has the disadvantage of high harmonic current, which makes it difficult to meet the IEC61000-3-2 Class C limits, and its application is greatly limited. This paper proposes and analyzes a single-switch integrated buck PFC converter. It is composed of buck and flyback PFC converter in input-parallel-output-parallel connection structure. Only one GaN switch and its control circuit are used, which reduces the cost of the converter. With critical conduction mode constant on time, the effect of dead zone of buck input current is eliminated by flyback unit. Taking advantage of buck and flyback PFC converters and excellent performance of GaN switch, the converter can achieve high efficiency and low total harmonic distortion over a wide voltage input range. This paper introduces the circuit structure, working principle and steady-state analysis. The correctness of the theoretical derivation is verified by PSIM simulation software. Finally, a 120W prototype with 94.1% peak efficiency is built to verify analysis results.