A radar tracking apparatus and method are provided. The radar tracking apparatus includes an α-β tracking filter, wherein the α-β tracking filter includes: a tracking index unit calculating a tracking index for obtaining α and β filter gains of an α-β tracking filter, based on changes in the measurement error covariance of a radar-measured value that occur when the measured value of target is converted from a polar coordinate system to a rectangular coordinate system; and a filter gain update unit calculating the variations of α and β filter gains, based on the partial differential coefficient of the changing rate of the α and β filter gains with respect to the changing rate of the tracking index and the variations of the tracking index, and updating the α and β filter gains.