A moving object detection apparatus repeatedly acquires, from a radar apparatus, observed-point information indicating observed-point positions that are positions of observed points where radar waves are reflected. The apparatus estimates, based on the observed-point positions indicated respectively by a plurality of pieces of the observed-point information and tracking filter coefficients indicating the degree of tracking the observed-point positions, a tracking trajectory tracking movement of a moving object corresponding to a plurality of the observed points. The apparatus determines whether distribution of the plurality of the observed points on both sides of the tracking trajectory is continuously biased to one side of the tracking trajectory. The apparatus sets the tracking filter coefficients so that the tracking degree is higher when the distribution of the plurality of the observed points is determined to be biased than when the distribution of the plurality of the observed points is determined to be not biased.