It has been known that the inertial dynamics has a little effect on the reaction rate in solutions. In this work, however, we find that for diffusion-controlled reactions between a ligand and a receptor on the cell surface there is a noticeable inertial dynamic effect on the reaction rate. We estimate the magnitude of the inertial dynamic effect by comparing the approximate analytic results obtained with and without the inertial dynamic effect included. The magnitude of the inertial dynamic effect depends on the friction coefficient of the ligand as well as on the relative scale of the receptor size to the distance traveled by the ligand during its velocity relaxation time.