The applications of adaptive arrays based on the digital beam forming technique are receiving wide attention. However, the adaptive control algorithm of the array antennas under TDMA systems is not well considered even though it requires particular consideration due to its intermittent bursts. In this paper, first, we propose a novel DOA (Direction of Arrival) estimation method which is suitable for TDMA bursts. Second, the HA (Howells-Applebaum) adaptive array based on the proposed DOA estimation method will be constructed for the terminals in the mobile communication systems using non-geostationary satellites . Then the performance of the DOA estimation method and the HA adaptive array will be examined through computer simulations and experiments.