Although time-domain oversampling of the received baseband signal is common for single-carrier transmissions, the counterpart of frequency-domain oversampling is rarely used for multicarrier transmissions. In this paper, we explore frequency-domain oversampling to improve the system performance of zero-padded OFDM transmissions over underwater acoustic channels with large Doppler spread. We use a signal design that enables separate sparse channel estimation and data detection, rendering a low complexity receiver. Based on both simulation and experimental results, we observe that the receiver with frequency-domain oversampling outperforms the conventional one considerably in channels with moderate and large Doppler spreads, and the gain increases as the Doppler spread increases. Although a raised-cosine pulse-shaping window can be used to improve the system performance relative to a rectangular window at the expense of data rate reduction, the performance gain is much less than that brought by frequency-domain oversampling in the considered OFDM system for Doppler spread channels.