Femtosecond oscillators with gigahertz (GHz) repetition rate are appealing sources for spectroscopic applications benefiting from the individually accessible and high-power comb line. The mode mismatch between the potent pump laser diode (LD) and the incredibly small laser cavity, however, limits the average output power of existing GHz Kerr-lens mode-locked (KLM) oscillators to tens of milliwatts. Here, we present a novel method that solves the difficulty and permits high average power LD-pumped KLM oscillators at GHz repetition rate. We propose a numerical simulation method to guide the realization of Kerr-lens mode-locking and comprehend the dynamics of the Kerr-lens mode-locking process. As a proof-of-principle demonstration, an LD-pumped Yb:KGW oscillator with up to 6.17-W average power and 184-fs pulse duration at 1.6-GHz repetition rate is conducted. The simulation had a good agreement with the experimental results. The cost-effective, compact and powerful laser source opens up new possibilities for research and industrial applications.