We studied why many diseases has multi-year period in their epidemiological dynamics, whereas a main source of the fluctuation is a seasonality with period of 1 year. Previous studies using a compartment model with seasonality in transmission rate succeed to generate a multi-year epidemiological dynamics, when, in particular, the seasonal difference is large. However, these studies have focused on the dynamical consequence of seasonal forcing in epidemiological dynamics and an adaptation of pathogens in the seasonal environment has been neglected. In this paper, we describe our study of the evolution of pathogen's sensitivity to seasonality and show that a larger fluctuation in the transmission rate can be favored in the life history evolution of pathogens, suggesting that multi-year periodicity may evolve by natural selection. Our result proposes a new aspect of the evolution of multi-year epidemics.