We present a very efficient Brownian dynamics (BD) method for evaluating inertial dynamic effects on diffusion-influenced reaction kinetics. The method requires only about 10 000 trajectories to yield a reliable estimate of the time-dependent rate coefficient. Another key advantage of the present ED method is that it requires only one set of ED simulations to calculate the rate coefficient for any value of the intrinsic rate constant. By using the proposed method, we show that the subtle inertial dynamic effect that may arise from the coupling between the center-of-mass and the relative motions of reactants is negligible.