A new parameterization of the accretion of cloud water by snow for use in bulk microphysics schemes is derived as an analytic approximation of the stochastic collection equation (SCE), where the theoretical collision efficiency for individual snowflake–cloud droplet pairs is applied. The snowflake shape is assumed to be nonspherical with the mass- and area-size relations suggested by an observational study. The performance of the new parameterization is compared to two parameterizations based on the continuous collection equation, one with the spherical shape assumption for snowflakes (SPH-CON), and the other with the nonspherical shape assumption employed in the new parameterization (NSP-CON). In box model simulations, only the new parameterization reproduces a relatively slow decrease in the cloud droplet number concentration which is predicted by the direct SCE solver. This results from considering the preferential collection of cloud droplets depending on their sizes in the new parameterization based on the SCE. In idealized squall-line simulations using a cloud-resolving model, the new parameterization predicts heavier precipitation in the convective core region compared to SPH-CON, and a broader area of the trailing stratiform rain compared to NSP-CON due to the horizontal advection of greater amount of snow in the upper layer. In the real-case simulations of a line-shaped mesoscale convective system that passed over the central Korean Peninsula, the new parameterization predicts higher frequencies of light precipitation rates and lower frequencies of heavy precipitation rates. The relatively large amount of upper-level snow in the new parameterization contributes to a broadening of the area with significant snow water path.