Underwater Visible Light Communication (UVLC) has great advantages of high transmission rate, large capacity, low latency, and low cost, which has become a feasible and attractive alternative in the field of underwater communication, with broad application prospects. However, UVLC performance is limited by bottleneck issues such as bandwidth limitations and various linear or nonlinear effects. In order to alleviate these problems, we studied geometrically-shaping based Amplitude Phase Shift Keying (APSK) modulation and coding mapping. A waveform-stage post equalizer based on Bidirectional Recurrent Neural Network (BRNN) is also proposed. In addition, a waveform-to-symbol receiver based on Deep Neural Network (DNN) is proposed to replace the traditional matching filtering, down-sampling, post-equalization and other operations. Compared with traditional receiver, the dynamic range of voltage using BRNN based post equalizer is improved by 170 mV(69%) and it is improved by 245 mV(100%) using waveform-to-symbol receiver based on DNN. In the paper, a waveform-stage post equalizer based on BRNN and a waveform-to-symbol receiver based on DNN are experimentally verified to be promising schemes in future UVLC.