Offshore oil production lies in facing difficulties caused by oil price decline and unexpected changes in global petroleum logistics. This paper suggests a stochastic model for optimizing the offshore oil production under uncertainty. The proposed model incorporates robust optimization and restricted recourse framework and uses the lower partial mean as measure of variability of the recourse profit. Some computational experiments and results using scenario-based data on the crude oil price and demand under uncertainty are presented. This study would be meaningful for the decision making in offshore oil production considering risks under uncertainty.