Semiconductor disk lasers (SDLs) have advantages of high output power and good beam quality. Their flexible external cavity provides convenience for inserting additional optical element to start mode locking and produce ultra-short pulse train with duration from picosecond to femtosecond. However, the very short lifetime in a range from about a few nanoseconds to tens of nanoseconds of the carrier in semiconductor gain medium limits the decrease of pulse repetition rate, thus restricting the increase of peak power of the mode-locked laser pulse to some extent. In this work, by using the relatively shallow In _0.2GaAs quantum wells, which have a relatively long carrier lifetime in the active region of gain chip, as well as the particularly designed semiconductor saturable absorption mirror (SESAM) that has a relatively small saturation flux, a passively mode-locked SDL with low repetition rate and high peak power is demonstrated. The used six-mirror cavity has a spot radius of about 200 μm on the chip and a 40 μm spot on the SESAM, and the total cavity length is about 1.92 m. The SESAM passively mode-locked SDL produces a stable pulse train with a lowest repetition rate of 78 MHz. When the temperature is 12 ℃ and the transmittance of the output coupler is T= 3%, an average output power value of 2.1 W and a pulse duration of 2.08 ps are achieved. The corresponding pulse peak power reaches 12.8 kW, which is about twice the reported highest peak power in an SESAM mode-locked SDL. When T= 2% and T= 5%, the obtained average output power values are 1.34 W and 1.62 W respectively, and the corresponding pulse peak power values are 8.17 kW and 9.88 kW. Based on the values reported in the literature and the results of pulse repetition rate in our experiments, the estimated lifetime of the carriers of the In _0.2GaAs quantum wells in the active region of the gain used chip is 16.4 ns. This high peak power mode-locked semiconductor disk laser has important potential applications in biomedical photonics, chemistry, and nonlinear microscopy.