In this study, an explicit incompressible scheme based on the Moving Particle Semi-implicit method (MPS) is applied to simulate slump flow. In the numerical method, the pressure Poisson equation is explicitly solved to obtain the pressure field. In simulating slump flow caused by fresh concrete, the fluid is treated to be non-Newtonian fluid and a regularized Bingham model is employed to calculate the viscosity. Flow characteristics in the slump flow are reproduced by the numerical method, and in good agreement with experimental measurements. The parameters including the rheological regularized parameter, yield stress, plastic viscosity, and particle distance, are examined in the simulations. It is found that the explicit incompressible scheme can well reproduce the concrete spreading. The yield stress in the rheology model affects the spreading distance significantly while the plastic viscosity plays an important role in the acceleration stage of the material spreading.