The present invention provides a single-segment linear constant-power LED (light-emitting diode) driving circuit and a method. The circuit includes a voltage input module, an LED load, a power switching tube, a sampling resistor, an overvoltage control module which is used for detecting the drain-end voltage of the power switching tube, a current control module which is used for limiting the peak current of the LED load, and a comparison module. According to the single-segment linear constant-power LED (light-emitting diode) driving circuit and the method, when input voltage is larger than the conduction voltage of the LED load, the current control module limits the peak current, so that a current average value in different input voltage periods can be constant; when the input voltage is larger than a set value, current flowing through the LED load is turned off, and therefore, power consumption can be decreased; and when the input voltage is smaller than the conduction voltage of the LED load, the LED load is turned off. According to the single-segment linear constant-power LED (light-emitting diode) driving circuit and the method of the invention, the control of average current in alternating current periods is realized by using a compensation capacitor, the peak current is limited, and therefore, constant power output in a wide input voltage range is realized; and the turn-off voltage and turn-off slope of the LED are adjusted through an external resistor, and therefore, the high efficiency of the system can be realized, and the electromagnetic interference performance of the system can be optimized.