We establish an equivalent circuit model of the GaN-based micro-LED system incorporating the parasitic parameters of the printed circuit board and bonding wires. Our deep analysis reveals that the parameters of intrinsic micro-LED significantly impact the modulation bandwidth of micro-LED. As the resistance and capacitance of micro-LED increases, the bandwidth of micro-LED decreases sharply. To address this critical issue, we propose several feasible strategies based on the analysis of the equivalent circuit model. In particular, we develop deep etching techniques to improve the bandwidth of the micro-LED system. By fitting the impedance parameters of the equivalent circuit model of shallow and deep etching micro-LEDs, the electrode capacitance of the deep-etching device is decreased by 24.9 pF compared to the shallow-etching device. This leads to a remarkable modulation bandwidth enhancement from 203 MHz to 249.8 MHz at a low current density of 4 kA/cm2. The high consistency of the simulated bandwidth from fitted parameters proves the validation and reliability of our proposed equivalent circuit model.