We have released a colloid simulator named KAPSEL implemented the “Smoothed Profile (SP) method” for direct numerical simulations of particulate flow. KAPSEL computes the fluid velocity and the electrostatics potential by solving both Navier-Stokes and Poisson equations directly. The time evolutions of the colloidal particles and the density of counter ions are then determined by solving Newton's equation of motion and advection-diffusion equation, respectively, in a consistent manner so that the electro-hydrodynamic coupling can be fully taken into account. The electrophoretic mobility of spherical colloidal particles is calculated in several situations including those in concentrated dispersions. The comparisons with theories show excellent quantitative agreements.