Code acquisition performance in the Direct-Sequence Code-Division Multiple-Access (DS/CDMA) communication system is strongly related to the quality of the communication systems. The performance is assessed by (i) code acquisition time; (ii) precision; and (iii) complexity for implementation. This paper applies the method of maximum likelihood (ML) to estimation of propagation delay in DS/CDMA communications, and proposes a low-complexity method for code acquisition. First, a DS/CDMA system model and properties of outputs with a passive matched-filter receiver are reviewed, and a statistical problem in code acquisition is mentioned. Second, an error-controllable code acquisition method based on the maximum likelihood is discussed. Third, a low-complexity ML code acquisition method is proposed. It is shown that the code acquisition time with the low-complexity method is about 1.5 times longer than that with the original ML method, e. g. 13 data periods under 4.96dB.