A new non-planar multi-pass laser amplifier based on the two-mirror ring optical path is proposed. It has the advantages of simple structure, small size, good space symmetry, easily adjustable and more amplification times. In the cavity of the amplifier, the signal beam goes through the laser medium many times for amplification along the three-dimensional non-planar symmetric path, and the high-power amplified laser can be obtained in a small-size laser medium. Theoretical modeling and parametric analysis of the optical path in the cavity of the amplifier are done. Simulation graphs for a portion of modes of optical path are given, optical loss and power amplification are also analyzed. A basic design of a solid-state non-planar multi-pass thin-disk laser amplifier based on Yb:YAG thin disk and laser diode (LD) end-pumping is given for high-power laser amplification.