In this study, we design a high-power compact solid-state picosecond pulse laser amplifier. We design a conducting-cooled end-pumped slab laser amplifier for which the gain medium is Nd∶YAG. We achieve the four-pass amplification of the picosecond pulsed laser through the slab multi-angle magnification technology. The influences of the selection of cutting angles of slat end face and laser incident angles on the filling factor and laser power amplification are analyzed. The output power of a mode-locked laser with 9.6-ps pulse duration and 100-kHz repetition rate respectively, is amplified up to 103 W; the single-pulse energy is 1.03 mJ.