We study effects of risk-averse attitude of both participators in aviation joint emergency response on the coevolution of cooperation mechanisms and individual preferences between airport and nonprofit organization. First, based on the current aviation joint emergency mechanism in China, we put forward two mechanisms to select the joint nonprofit organization, including reputation cooperation and bidding competition. Meanwhile, we consider two preferences including altruism and selfishness. Then we build replicator dynamics equations using the theory of conditional value-at-risk (CVaR) taking risk aversion attitude into account. Finally, we introduce the factor of government and give all participators some suggestions. We show that the risk-averse attitude of the other game participator affects the one participator's decision and the effects subject to some parameters.