The novel high power micro-gravity heat pipes are applied for the conduction cooling of a high power and high repetition space-based all-solid-state laser. The waste heat of laser amplifiers can be dissipated effectively and thereby the laser output with high beam quality and high power is obtained. In view of the pumping laser diode (LD) stacks and slab gain medium being major thermal sources in slab amplifiers, the novel amplifier structures for heat dissipating are designed. In the experiment, the heat-sinking capability of two stage simulated amplifiers in series is measured with the single-channel micro-gravity heat pipe and the two-channel micro-gravity heat pipe, respectively. The experimental results show that the temperature of both stage pre-amplifiers stabilizes in the range of operating temperature for the laser diode array. In the end, the average output power more than 20 W, magnification times greater than 20, M2x of 1.42 and M2y of 1.31 are achieved successfully.