In this paper, with focusing particular attention on a major issue — the lack of consistency conditions on the spatial discretization schemes of the existing MPS method, we develop a new meshfree particle method named Least Squares Moving Particle Semi-implicit/Simulation (LSMPS) method. The new schemes have arbitraly higher order consistency conditions, make treatment of boundary conditions exceedingly easy, and can be applied for both Eulerian and Lagrangian framework. Moreover, applications of the new schemes for numerical analysis of incompressible flows with the free surfaces result in enhancement of numerical accuracy and stability.