A primary‐side controlled high‐precision constant current AC–DC LED driver, based on source‐driving control scheme, is designed for low‐power LED‐lighting applications in this study. The ratio between demagnetisation time T_Demag and switching period T_S and the primary peak current are remained constant by the proposed control IC, obtaining constant current output. Meanwhile, an adaptive line voltage compensation circuit, integrated in the primary peak current controller, is proposed based on source‐driving control scheme. A compensation current proportional to line voltage is injected to the primary‐side current sampling pin CS, thus making the turn‐off bandgap reference of primary peak current under high‐line voltage lower than that under low‐line voltage. As a consequence, overshoot phenomena of primary peak current can be avoided, and the line regulation as well as the precision of output current can be improved. The proposed control IC has been fabricated in TSMC 0.35 μm 5 V/650 V CMOS/LDMOS process. Experimental results of a 5 W prototype show that the output current is kept stable at ∼250 mA, and the line regulation is within ±0.5% in a wide range of universal‐input ac voltage from 85 to 264 V, and that >80% efficiency is obtained under heavy LED loads.