An insulation resistance measuring apparatus designed to calculate a complex impedance of an ac circuit including a measuring resistor, a coupling capacitor, an insulation resistor installed in a vehicle, and a ground capacitance. The insulation resistance measuring apparatus includes a sine wave current applying device which applies an ac signal to the measuring resistor and measures a voltage change appearing at a junction of the sine wave current applying device and the measuring resistor. The ac signal and the voltage change are used to determine the complex impedance. A resistance value of the insulation resistor is calculated as a function of the complex impedance. This structure enables the circuit to be reduced in size.