The post-equalizer in the Underwater Visible Light Communication (UVLC) system can overcome the nonlinear distortion existing in the system. The existing nonlinear post-equalizer based on deep learning still has problems such as the number of data nodes has a great influence on the effect, the equalization effect decreases significantly when the data rate becomes higher and too complex a model leads to slow training time. In this paper, we propose a Dual Self-Attention Network (DSANet) as a post equalizer in the CAP modulated UVLC system. Experiments show that the DSANet-based post equalizer can achieve good equalization performance at different data rates; it shows strong robustness when the number of data nodes changes; its training speed is close to that of the plainest nonlinear post-equalizer.