This paper presents an investigation of a channel tracking based passive time reversal (PTR) communication method for mobile single-input/multiple-output communications in rapidly time-varying underwater acoustic channel. To investigate its performance in the non-stationary channels, the method is applied to a synthetic dataset generated by the underwater acoustic moving source model using normal mode method. The transmitted signal is modulated by the single-carrier modulation scheme using the carrier frequency of 20 kHz and bandwidth of 4, 8, and 12 kHz. From the comparisons with conventional PTR approach, the following advantages were found: (1) the quality of the equalization result hardly degrades even if the sound source moving speed increased, (2) suboptimal diversity combining is performed in the sense of the energy utilization of the multipath, (3) the dependence on the bandwidth is relatively small, and a significant performance improvement is seen especially for narrowband signals.