In the underwater acoustic (UWA) channel, the line-of-sight (LOS) path has the characteristics of stable magnitude and continuous phase, which is seldom affected by the surface/bottom reflection. Therefore, in the direct sequence spread spectrum (DSSS) communication systems, the receiver usually extracts the LOS path to recover the information bits and achieve the robust communication. However, the UWA channel is typically the doubly spread channel, i.e., multipath fast fading and non-uniform Doppler shifts, which seriously degrades the performance of extracting the LOS path by the conventional maximum energy method. Therefore, this paper proposes a LOS peak detection and tracking algorithm to extract the LOS path in the UWA DSSS communications. In the proposed algorithm, the candidate correlation peaks after de-spreading are firstly selected by the adaptive peak detection threshold. Then, according to the transmitter/receiver motion relationship, the Delay-Doppler joint state equation is established, and thus the nearest neighbor method adopting the Kalman filter is proposed to track the LOS path. Numerical simulation results demonstrate that the proposed algorithm has better processing performance in the doubly spread channels compared with the conventional method. Finally, the performance of the proposed algorithm is confirmed by the shallow water horizontal channel and deep sea vertical channel experiments.