In a tracking apparatus for tracking an object by the use of a plurality of detecting data sets supplied from a detecting device, a velocity presuming portion is provided together with a position presuming portion. The position presuming portion finds a presumed position of the object at the latest detecting time of the detecting data sets by the use of the latest detecting time and regression curves found on the basis of the detecting data sets. The velocity presuming portion finds a presumed velocity of the object at the latest detecting time by the use of the regression curves and at least one of former detecting times different from the latest detecting time.