The bullwhip effect refers to the phenomenon where demand variability is amplified when one moves upward a supply chain. In this paper, we exactly quantify the bullwhip effect for cases of seasonal demand processes in a two-echelon supply chain with a single retailer and a single supplier. In most of the previous research, some measures of performance for the bullwhip effect are developed for cases of non-seasonal demand processes. The retailer performs demand forecast with a multiplicative seasonal mixed model by using the minimum mean square error forecasting technique and employs a base stock policy. With the developed bullwhip effect measure, we investigate the impact of seasonal factor on the bullwhip effect. Then, we prove that seasonal factor plays an important role on the occurrence of the bullwhip effect.