We demonstrate a self-starting Kerr-lens mode-locked (KLM) Yb:YAG thin-disk oscillator operating in the regime of positive intracavity group-delay dispersion (GDD). It delivers 1.7 ps pulses at an average power of 17 W and a repetition rate of 40 MHz. Dispersive mirrors compress the pulses to a duration of 190 fs (assuming sech2 shape; Fourier limit: 150 fs) at an average power level of 11 W. To our knowledge, this is the first KLM thin-disk oscillator with positive GDD. Output powers of up to 30 W were achieved with an increased output coupler transmission and intracavity GDD. We demonstrate increase of the pulse energy with increasing positive intracavity GDD, limited by difficulties in initiating mode-locking.