The phased array antenna has the ability to perform adaptive sampling by directing the radar beam without inertia in any direction. The adaptive sampling capability of the phased array antenna allows each sampling time interval to be varied for each target, depending on the acceleration of each target at any time. In this paper we design a three-dimensional adaptive tracking algorithm for the phased array radar system with a given set of measurement parameters. The tracking algorithm avoids taking unnecessarily frequent samples, while keeping the angular prediction error within a fraction of antenna beam width so that the probability of detection will not be degraded during a track update illuminations. In our algorithm, the target model and the sampling rate are selected depending on the target range and the target maneuver status which is determined by a maneuver detector. A detailed simulation is conducted to test the validity of our tracking algorithm for encounter geometries under various conditions of maneuver.