A primary-side regulation (PSR) constant current (CC) output and constant voltage (CV) output AC–DC converter is proposed and an adaptive high-precision closed-loop constant current control scheme is put forward in this paper. In the CC mode, the converter adopts the closed-loop control strategy to realize that the switching period adaptively converges to twice the demagnetization time, which realizes the CC output. In addition, exactly detecting the demagnetization time is a prerequisite for obtaining a high-precision output current. Therefore, a demagnetization time detection circuit is designed to provide accurate and reliable demagnetization information. The control IC was fabricated with the Nuvoton 0.5um BCD process, and a 5 V/2 A prototype circuit was implemented to verify its performance. Experimental results show that the CC deviation is within ± 1.4%, which is lower than the target value of ± 2.0%. Under different loads and AC inputs, the conversion efficiency in the CC mode varies between 76.3% and 80.7%.