This study proposes the method that most effectively suppresses numerical diffusion, based on numerical analyses using a stabilized Material Point Method (MPM) formulated with an implicit u–p scheme. In this method, the momentum conservation equations for the two-phase mixture and the continuity equation for pore water are solved simultaneously in a fully coupled manner. Under low-permeability conditions, pressure oscillations can occur if the arrangement of unknowns does not satisfy the Ladyzhenskaya–Babuska–Brezzi (LBB) condition. To address this issue, stabilized MPMs have been proposed, one of which is the Fluid Pressure Laplacian (FPL) method. In the FPL approach, a stabilization term is added to the weak form of the pore water continuity equation, and a known pore water pressure term appears in the discretized equations at the grid nodes. Therefore, it is necessary to reconstruct the pore pressure values at the end of the previous time step by projecting them from material points to grid nodes. In this study, verification examples were conducted using the stabilized MPM with the FPL method, where the projection method for pore pressure and the functions used for projection and interpolation were varied. The results show that using Taylor Particle-In-Cell (TPIC) method for pressure projection, combined with linear functions for interpolation, leads to the highest accuracy in pore pressure reconstruction, effectively suppressing numerical diffusion.