A failure prediction system includes: a processor, the processor being configured to: collect torque values of a drive axis of a robot that is operating in accordance with a given work program; derive an evaluation formula approximating a time change of the torque value which is most recent from among the collected torque values set a failure threshold that is the torque value at which it is determined that failure of the drive axis occurs, based on the evaluation formula and the time change of the torque value when the drive axis reached failure in the past; and calculate an estimated value for the torque value when a prediction time set in advance has elapsed in the evaluation formula, and determines whether failure of the drive axis is predicted within the prediction time according to comparison between the estimated value and the failure threshold.