Blind beamforming based on the maximum signal-to-noise ratio (MSNR) can improve the performance of an array system only when the processing gain of the given code-division multiple-access (CDMA) system is high enough such that the desired signal can become dominant after despreading (see Choi, S. and Shim, D., IEEE Trans. Veh. Technol., vol.49, p.1793-1806, 2000; Choi, S. and Yun, D., IEEE Trans. Antennas Propagat., vol.45, p.1393-1404, 1997). We consider a maximum signal-to-interference-plus-noise ratio (MSINR) beamforming. The MSINR performance criterion is chosen to deal with strong interferers effectively. It is shown that blind MSINR beamforming is possible by directly utilizing the input and output signals of correlators of the CDMA systems. In addition, we propose an adaptive beamforming algorithm at a lower computational complexity - about O(7.5N) - where N is the number of antenna elements of the array system. Simulation results are presented in various signal environments to show the performance of the proposed adaptive algorithm.