Blue/green light-emitting diodes (LEDs) have been studied extensively in medium/short-distance underwater optical wireless communication (UOWC), while available commercial bandwidth-limited LEDs cannot support the increased capacity. In this work, a 175-µm blue mini-LED with a high 3 dB modulation bandwidth of 580 MHz was designed and employed to implement a high-speed UOWC system to improve the bandwidth while maintaining high emitting optical power. As a result, we achieve the data rate of 3.8 Gb/s and the rate-distance product of 7.6 Gb/s•m of the PAM-4 signal with the 3.7e-3 bit error rate (BER) over the 2-m underwater channel by using a single-pixel 175-μm GaN-based mini-LED and an avalanche photodiode (APD). To the best of our knowledge, it is the highest rate-distance product among the UOWC systems based on a single-pixel LED and a single APD. In addition, we design multiple sets of comparison experiments to provide a comprehensive investigation regarding channel loss, transmission capacity, and computation complexity between the UOWC system with and without water.