This paper proposes an adaptive algorithm for adaptive arrays that minimizes the bit error rate (BER) of the array output signals in radio communication systems with the use of multilevel modulation signals. In particular, amplitude phase shift keying (APSK) is used as one type of multilevel modulations in this paper. Simultaneous non-linear equations that are satisfied by the optimum weight vector of the proposed algorithm are derived and used for theoretical analyze of the performance of the adaptive array based on the proposed algorithm. As a result of the theoretical analysis, it can be shown that the proposed adaptive array improves the carrier to interference ratio of the array output signal without taking advantage of the nulls. Furthermore, it is confirmed that the result of the theoretical analysis agrees with that of computer simulation. When the number of the received antenna is less than that of the received signals, the adaptive array based on the proposed algorithm is verified to achieve much better performance then that based on the least mean square (LMS) algorithm.