A high-power diode-pumped pure Kerr-lens mode-locked Yb:KGW laser was demonstrated. The developed laser delivered 240 fs pulses with 2.3 W of average output power at a repetition rate of 86.8 MHz. Shorter pulses of around 120 fs with 1.2 W of average output power were also generated. The self-starting operation of the oscillator was demonstrated. The limiting factor to the laser operation was the appearance of a strong continuous wave component in the mode-locked laser spectrum.