Direct sequence spread spectrum (DSSS) signals are now widely used in air and underwater acoustic communications. A receiver which does not know the pseudo-random (PN) sequence cannot demodulate the DSSS signal. In this paper, firstly, the principle of principal component analysis (PCA) for PN sequence estimation of the DSSS signal is analyzed, then a modified online unsupervised learning machine (LEAP) is introduced for PCA. Compared with the original LEAP, the modified LEAP has the following improvements: (1) By normalizing the system state transition matrices, the modified LEAP can obtain better robustness when the training errors occur; (2) with using variable learning steps instead of a fixed one, the modified LEAP not only converges faster but also has excellent estimation performance. When the modified LEAP is converging, we can utilize the network connection weights which are the eigenvectors of the autocorrelation matrix of the DSSS signal to estimate the PN sequence. Due to the phase ambiguity of the eigenvectors, a novel approach which is based on the properties of the PN sequence is proposed here to exclude the wrong estimated PN sequences. Simulation results showed that the methods mentioned above can estimate the PN sequence rapidly and robustly, even when the DSSS signal is far below the noise level.