In recent years energy storage systems (ESSs) have been used widely in most European and American countries because of their economic and technical benefits. One of their most exciting capabilities is the ability to participate in deregulated power markets. This paper proposes a hybrid stochastic-robust optimization approach, in which an ESS owner can engage in energy arbitrage in the day-ahead market (DAM) and provide extra bids and offers in the real-time market (RTM) to increase his profit. Stochastic programming is used to model DAM price uncertainties, while the robust optimization approach is proposed for more conservative decision making in RTM considering its high volatile prices. The results are optimal price-quantity pairs, which should be submitted to the DAM and RTM by the ESS owner.