Time evolution of particle size distribution of fractal agglomerates undergoing Brownian coagulation in the free-molecule regime was investigated. A simple analytical solution for the size distribution change was obtained by using the assumption that the size distribution during the coagulation process can be represented by a time-dependent log-normal function. The derived solution consists of three parameters of the log-normal distribution function. This study is believed to provide the first analytical solution for all the parameters of the log-normal distribution of fractal agglomerates undergoing coagulation in the free-molecule regime. To validate the derived solution, numerical computations were performed. The results were compared with the analytical solution and good agreement was obtained.