Abstract: In underwater acoustic communication, block-wise equalizers exhibit low complexity but limited performance. This paper presents a block-wise sparse equalizer (BSE) designed for underwater acoustic single-carrier communication. The method takes into account the sparse characteristics of equalizer taps, which distinguishes it from traditional counterparts. It achieves iterative estimation of sparse equalization vectors under the assumption of time-invariant channel through variational Bayesian inference. The model is then extended to the time-varying scenario, and a basis expansion model-based BSE is proposed. This transforms the estimation of the time-varying equalization matrix into the estimation of time-invariant sparse basis coefficient vectors, thereby improving the robustness of the system. Compared to classical block-wise equalizers, the proposed method tackles the inverse problem of channel estimation by directly estimating the equalization coefficient vectors. In addition, it takes into account the sparsity of the equalizer taps. Simulation and experimental results demonstrate the effectiveness of the method under sparse channels and its robustness under time-varying conditions.