The hybrid action of quantum-dot saturable absorber and Kerr-lens mode locking in a diode-pumped Yb:KGW laser was demonstrated. Using a quantum-dot saturable absorber with a 0.7% (0.5%) modulation depth, the mode-locked laser delivered 90 fs (93 fs) pulses with 3.2 W (2.9 W) of average power at the repetition rate of 77 MHz, corresponding to 462 kW (406 kW) of peak power and 41 nJ (38 nJ) of pulse energy. To the best of our knowledge, this represents the highest average and peak powers generated to date from quantum-dot saturable absorber-based mode-locked lasers.