We propose and experimentally demonstrate an underwater wireless optical communication (UWOC) system using a 520-nm laser diode (LD) and 32-quadrature amplitude modulation (32-QAM) single carrier signals. To mitigate the inter-symbol interference (ISI), a frequency domain equalizer combined with a time-domain decision feedback noise predictor is employed at the receiver. However, this structure cannot apply channel coding conjunctively. Therefore, an interleaver/deinterleaver pair is applied to handle the decoding delay, and thus systematic Reed-Solomon (RS) code can provide reliable feedback signals. With a 3-dB bandwidth of 200 MHz, the proposed system with the frequency domain equalization and noise prediction (FDE-NP) scheme can achieve a maximal net data rate of 3.48 Gbps, which is 17.2% higher than that of orthogonal frequency division multiplexing (OFDM) scheme. At a net data rate of 3.31 Gbps, we have successfully achieved a transmission distance up to 56 m. To the best of our knowledge, this is the first time to employ FDE-NP in UWOC where OFDM conventionally plays a prevailing role for high-speed transmission.