A higher order Laplacian model is proposed for enhancement and stabilization of pressure calculation by the MPS method. The higher order Laplacian model is derived by taking the divergence of a particle-based gradient model. The proposed higher order Laplacian is then applied for discretization of both Laplacian of Poisson pressure equation and that of the viscous forces in the CMPS-HS method. A few numerical tests, namely, exponentially excited sinusoidal pressure oscillations and a violent sloshing flow are carried out to demonstrate the enhancing and stabilizing effect of the proposed higher order Laplacian model.