We have been proposed a direct numerical simulation scheme for colloidal dispersions [Phys.Rev.E 71,036707 (2005)]. We improved the previous scheme and formulated a full explicit time-marching, called "Smoothed Profile (SP) method". SP method as a direct numerical simulation of particulate flow provides a way to couple continuum fluid dynamics with rigid-body dynamics through smoothed profile of colloidal particles. Moreover, SP method is extended to multi-component fluids, such systems as charged colloids in electrolyte solutions. Dynamics of colloidal dispersions is solved as much computational cost as required for solving non-particulate flows. Numerical results which assess hydrodynamic interactions of colloidal dispersions are presented to validate SP method. SP method is not restricted to any constitutive model of the host fluids. Henceforth, it can be applicable to colloidal dispersions in complex fluids.