In　order　to　obtain　high　laser　pulse　energy,　a　laser　amplifier　system　was　designed.　The　parameters　of　the　amplifier　system　are　studied　such　as　the　output　energy,　pulse　width,　energy　stability　and　output　pulse　width.　First,　the　analysis　of　the　four-level　laser　rate　equation　is　carried　out,　and　the　relations　between　pump　energy,storage　energy,　and　gain　coefficient　are　derived.　Then,　the　system　design　of　the　laser　amplifier　is　given,　and　the　experimental　verification　is　carried　out.　Finally,　the　performance　index　of　the　output　laser　is　tested.　Experimental　results　indicate　that,　at　the　size　of　the　Nd:YAG　crystal　rod　of　φ8　mm×100　mm,　the　doping　concentration　Nd3+　of　1.1%,　the　pump　maximum　power　of　24　kW,　the　semiconductor　thermoelectric　refrigeration　with　three　maximum　power　of　66　W,　the　repetition　frequency　of　10　Hz,　the　pump　current　of　80　A,　the　pump　pulse　width　of　200　μs,　we　obtained　the　output　of　the　laser　with　the　maximum　pulse　energy　of　1　050　mJ　at　a　wavelength　of　1　064　nm,　a　pulse　width　of　10　ns　and　an　output　energy　instability　of　3%.　The　beam　qualities　M2　horizontal　and　vertical　directions　are　3.9　and　4.8,　respectively,　through　the　beam　quality　diagnostic　instrument　M-200S.　It　can　satisfy　the　system　requirements　of　high　energy,　without　water-cooling,　stability　and　reliability.　©　2019,　Science　Press.　All　right　reserved.