A three-dimensional simulation model for colloidal dispersion system with an adsorptive surface under a specified bulk concentration was developed basing on the Brownian dynamics technique, and the adsorption process of electrostatically stabilized colloidal particles with radius of 50 nm onto a planar surface with counter charge was simulated. The particle-particle and particle-surface interactions were modeled on the DLVO theory. The adsorbed particles are found to form hexagonally ordered array, only if the surface coverage is above a certain threshold, which varies depending on the ionic strength or the interaction potentials. Through the analysis of the ordered structure, we found that the determinant factor for the order formation is "one-directional average force" acting between adsorbed particles, which exhibits a common value regardless of the ionic strength. Also, looking at the last process for establishing the order, we developed a model that can predict the potential barrier for the order formation. Further, the order formation was proven to be a stochastic phenomenon, and a model to describe the probability against time was developed and its quantitative validity was demonstrated. (c) 2005 Elsevier Ltd. All rights reserved.