This paper proposes a novel equalization algorithm for underwater communication. It performs iteratively adaptive equalization and channel decoding in order to reduce intersymbol interference (ISI). In particular, our proposed forward-backward turbo equalizer uses two sparse feedforward-feedbackward equalizers operating in opposite time directions, each sparse equalizer performing jointly phase synchronization to enhance the overall performance. Our simulations, both on synthetic and real underwater channels validate the effectiveness of the proposed scheme as they show a considerable gain compared to the conventional adaptive turbo equalization algorithm.