Superposition coding (SC) with successive interference cancellation (SIC) is considered a promising non-orthogonal multiple access (NOMA) technique for improving spectral efficiency recently. In contrast, the residual interference after SIC at the receiver severely degrades the BER performance when applied in underwater acoustic (UWA) channels. In this paper, we propose a receiver that combined SIC and turbo equalization for superposition coding based downlink UWA orthogonal frequency-division multiplexing (OFDM) system, where a near-far user pair is mainly considered. We design an SC signal detector based on the minimum mean square error (MMSE) algorithm and eliminate the far user information with high power after detection. After SIC, the turbo equalization composed of an MMSE equalizer and LDPC decoder is adopted for the near user symbols with residual interference from the SIC process. Simulation results and recorded data from the Yellow Sea, China, show that the proposed receiver has a performance gain of at least 1 dB under different modulation pairs compared with traditional SIC receiver based on maximum a posteriori probability principle (MAP SIC). The error-free two-user downlink communication result shows a maximum sum-rate of 8kbps over the horizontal range of downlink 3.55km has been achieved in the Yellow Sea test.