While underwater acoustic (UWA) communication offers a practical way to establish a wireless link with underwater vehicles, designing a UWA communication system onboard a small autonomous underwater vehicle (AUV) still poses significant challenges. As the adoption of the low-complexity, robust noncoherent communication technology is limited by low bandwidth efficiency and a low data rate, coherent UWA communication requires Doppler mitigation and channel equalization measures to achieve a relatively high data rate in a moving state. Due to the strict constraints of a small-scale AUV in terms of resources and energy consumption, it is not appropriate to use high-complexity Doppler/multipath compensation technology from the prospect of system implementation. In this paper, an efficient and low-complexity UWA differential binary phase-shift keying (DBPSK) system onboard a small AUV is proposed by simplifying the Doppler and multipath compensation. Specifically, for Doppler, the delay of the adjacent DBPSK symbols is calculated according to the Doppler estimate to facilitate delay-tuning Doppler correction. For multipath, low-complexity LMS channel equalization is incorporated with error correction coding to enable multipath mitigation. With a simple structure and low computational complexity, the proposed scheme facilitates the practical hardware implementation and system integration in the small AUV platform. The numerical simulations are conducted to assess the validity of the proposed scheme under different channel conditions and the effectiveness of the proposed scheme is further verified by two UWA communication field tests, which are performed at a practical shallow water sea and lake, respectively.