A motor drive apparatus includes a rectifier which converts AC power to DC power and DC power to AC power, an inverter which converts the DC power output by the rectifier to AC power and supplies the AC power to a motor, and which converts regenerative power from the motor to DC power and returns the DC power to the rectifier, a DC voltage detection unit which detects a DC output voltage of the rectifier, an AC voltage detection unit which detects an AC output voltage of the rectifier, a frequency calculation unit which calculates the frequency of the AC voltage; a storage unit which stores as a reference value the DC voltage at the start of the regenerative operation, and a power failure detection unit which determines the presence or absence of a power failure by using the DC voltage, the reference value, and the AC voltage frequency.