The jumps in population size due to the occurrence of an unfavorable physical environment (e.g. the effects of periodic climate disaster on the population size), or due to the intrinsic physiological and reproductive mechanisms of the population (e.g. the seasonal reproduction of most animal populations), can be called impulsive perturbations. A two-phenotype evolutionary game dynamics with impulsive effects is investigated. The main goal is to show how the evolutionary game dynamics is affected by the impulsive perturbations. The results show that the impulsive perturbations not only result in periodic behavior, but also it is possible that an ESS strategy based on the traditional concept of evolutionary stability can be replaced successfully by a non-ESS strategy.