Actin filaments are the most abundant component of cellular cytoskeleton. To understand actin polymerization is important in the field of cell biomechanics. The purpose of this study is to develop the computational simulation system to calculate actin polymerization dynamics from a single actin monomer to many filaments. We propose a mathematical model describing actin monomers polymerization to the tip of barbed ends of actin filaments, using Brownian dynamics method. Results obtained from this model are 1) dependency of actin concentration on actin filament elongation rate, and 2) the process of assembling and elongation in actin filaments.