A　time　marching　algorithms,　which　used　to　solve　incompressible　internal　flow　field　of　turbomachinery　was　developed.　By　using　Chorin＇s　method　of　artificial　compressibility,　the　control　equations　were　transformed　from　elliptic　type　into　hyperbolic　systems　in　order　to　extend　the　time　marching　technique　to　very　low　Mach　number　flows.　Viscous　effects　could　be　predicted　by　using　a　thin　shear　layer　approximation　to　the　N-S　equations　and　Baldwin-Lomax　eddy　viscosity　turbulence　model.　Some　accelerating　convergence　techniques　such　as　multi-grid　and　local　time　step　method　were　employed.　Application　to　a　flow　field　within　a　low-solidity　rocket　pump　inducer　were　presented　and　discussed.　The　calculated　results　indicate　that　the　techniques　can　be　used　to　predict　the　incompressible　internal　flow　field　of　turbomachinery.