The Brownian dynamics (BD) method for diffusion-influenced bimolecular reactions, which was proposed by Lee and Karplus, is implemented to calculate the time-dependent rate coefficient k(f)(t). It is shown that the present method gives quick estimates of k(f)(t) by using just about 5000 trajectories. Compared to the previous method due to Zhou, which has a similar efficiency and accuracy, the present method has a key advantage. It requires only one set of BD simulations to calculate the time-dependent rate coefficients for any value of intrinsic rate constant, while Zhou's method requires separate sets of BD simulations for different intrinsic rate constants.