Pseudo-particle modeling (PPM) is a particle method (PM) proposed in 1996. Though it is effective for the simulation of microscopic particle-fluid systems, its application to practical systems is still limited by computational cost.In this note, we speed up the computation by using a combination of weighted averaging with finite difference techniques to upgrade the particle interactions to a fluid element level, which conforms to the Navier-Stokes equation. The approach, abbreviated to MaPPM, is then applied to the problem of one-dimensional Poiseuille flow with a quantitative comparison to the results of another related PM smoothed particle hydrodynamics (SPH), where the accuracy and efficiency of MaPPM is found to be much better than that of SPH. Flows around a cylinder and multiple freely moving particles are also simulated with the new model, resulting in reasonable flow pattern and drag coefficient. The convergence and robustness of the algorithm prove promising.``