Abstract: A novel slightly compressible model(SCM) is very efficientfor low Mach number flow, in which it does not have to satisfy thedivergence-free condition in order to get the solutions of theincompressible Navier-Stokes equation by time marching method. Theefficiency and precision of SCM is studied. Preconditioning technique hasbeen introduced into SCM for acceleration of convergence. Then thepreconditioned equations and its characteristic system including thepreconditioned construct of flux are recommended. By numerical simulationswith the cases of circular cylinder, cavity flow, NACA0012 and 6:1 prolatespheroid, SCM is proved to be efficient and precise; on the other hand, itshows that preconditioning technique plays an important role in accelerationof convergence and improves the precision of results. SCM would be appliedto engineering simulations in the future.