Conventionally, code acquisition with antenna array employs a correlator bank and the serial-search technique. Due to the inherent properties of correlators and serial search, mean acquisition time of the correlator-based approach is large, especially in strong interference environments. Recently, an adaptive-filtering approach has been applied to code acquisition. This method simultaneously performs beamforming and code-delay estimation with a spatial and a temporal filter. Its performance is significantly better than that of the correlator-based approach. However, its computational complexity will be high when the code-delay uncertainty is large. In this paper, we propose a low-complexity adaptive-filtering scheme to solve the problem. Incorporating a serial-search technique, we are able to significantly reduce the size of the temporal filter, so does the computational complexity. We also analyze the proposed algorithm and derive closed-form expressions for optimum solutions, mean-squared error, and mean acquisition time. Simulations show that while the proposed system somewhat compromises the performance, the computational complexity is much lower that of the original adaptive-filtering approach.