We introduce a multiscale mathematical model for simulating ligand-receptor binding, dissociation and transport in blood circulation using a group of nonlinear differential equations. It is assumed that the biological interactions take place in capillaries, ligands bind and dissociate with receptors on the wall of capillary, and ligands are transported by blood stream. The blood stream in capillary is modeled as Newtonian laminar flow, and ligand transport is modeled by a general transport equation. A set of ordinary differential equations is used to describe the complex chemical kinetics due to binding and dissociation. The time-dependent solution of media flow is obtained using second order implicit Euler method to achieve high order time accuracy. The spatial distribution of ligands and receptors are obtained and visualized. Findings from this study have implications with regard to tumor growth and vascular diseases.