Visible light communication (VLC) based on laser diodes demonstrates great potential for high data rate maritime, terrestrial, and aerial wireless data links. Here, we design and fabricate high-speed blue laser diodes (LDs) grown on c-plane gallium nitride (GaN) substrate. This was achieved through active region design and miniaturization toward a narrow ridge waveguide, short cavity length, and single longitudinal mode Fabry–Perot laser diode. The fabricated mini-LD has a low threshold current of 31 mA and slope efficiency of 1.02 W/A. A record modulation bandwidth of 5.9 GHz ($-3\mathrm{dB}$) was measured from the mini-LD. Using the developed mini-LD as a transmitter, the VLC link exhibits a high data transmission rate of 20.06 Gbps adopting the bit and power loading discrete multitone (DMT) modulation technique. The corresponding bit error rate is 0.003, satisfying the forward error correction standard. The demonstrated GaN-based mini-LD has significantly enhanced data transmission rates, paving the path for energy-efficient VLC systems and integrated photonics in the visible regime.