A coagulation coefficient of agglomerates with different fractal dimensions has not been considered in the past, even though there is a possibility of variations in the fractal dimension of agglomerates at any instant. In this study, a Brownian dynamics simulation was performed with simultaneous collision and sintering, and variations in the fractal dimension of agglomerates were observed. A coagulation coefficient expression for agglomerates with two different fractal dimensions was proposed. The coagulation coefficient based on the different fractal dimensions was at most 140% higher than that based on the average fractal dimension. To determine an accurate coagulation coefficient of agglomerates, the fractal dimension of each agglomerate has to be considered.