This paper presents a Cournot duopoly model based on a condition when firms are facing cost uncertainty under risk neutrality and risk aversion. Each firm conjectures about the rival’s output level, and its cost function is assumed to be unknown to its rival. The Cournot model shows that the expected utility maximizing firms, under risk aversion, show different behaviors from the expected profit maximizing firms. This implies that each firm can increase or decrease its output, which depends on the interaction between both firms under cost uncertainty, assuming that both firms are risk- averse.