We report on the dissipative soliton operation of a diode-pumped single-crystal bulk Yb:KGW laser oscillator in the all-positive-dispersion regime. Stable passively mode-locked pulses with strong positive chirp and steep spectral edges are obtained. The spectral centering at 1038.6 nm has a bandwidth of about 6.9 nm, and the chirped pulses have a pulse duration of 4.317 ps. The maximum average power can be up to 2.07 W when pumped by absorbed pump power of 5.3 W. The mode-locked slope efficiency and optical–optical conversion efficiency are shown to be 62% and 39%, respectively. Considering the pulse repetition rate with a value of 52 MHz, the corresponding pulse energy is estimated to be 39.8 nJ.