An LED constant-current drive circuit includes a BUCK circuit consisting of a transformer T1, a diode D9, a capacitor C5 and a field effect transistor Q1; a voltage limiting circuit consisting of a resistor R1, a diode D8, a capacitor C1, a resistor R3, a triode Q2, a zener diode DZ1 and a diode D10; and a current limiting circuit consisting of a resistor R4, a triode Q3, a triode Q4 and a resistor R2. When the transistor Q1 is turned on, a current flows through a primary side of the transformer T1 and an LED load, and then flows through the transistor Q1 and the resistor R2, and then flows back to a negative electrode of a power supply. When the transistor Q1 is turned off, the current flows through the primary side of the transformer T1, the LED load and the diode D9, thus forming a loop.