A fan speed control circuit is used for controlling rotation speed of a fan. The fan speed control circuit receives a pulse width modulation (PWM) signal from a system and comprises a programmable control unit and a current control unit. The programmable control unit receives the PWM signal, is connected to a Hall element for receiving a voltage signal therefrom, and provides a control signal. The current control unit takes the control signal to control current flowing through a stator coil unit of the fan so as to control the speed of the fan. The programmable control unit has a program written for the PWM signal, and when the fan speed control circuit is used in another system with a different PWM signal, the programmable control unit can be given a new program for the different PWM signal for controlling the speed of the fan.