DPM (Dynamic Power Management) is an effective technique for reducing the energy consumption of embedded systems that is based on migrating to a low power state when possible. While conventional DPM minimizes the energy consumption of the embedded system, it does not utilize the properties of the power source. Alternative power sources such as fuel cells (FCs) have substantially different power and efficiency characteristics that have to be taken into account while developing policies that maximize their operational lifetime. In this paper, we present a new DPM policy for embedded systems powered by FC based hybrid source. We develop an optimization framework that explicitly considers the FC system efficiency and is aimed at minimizing the fuel consumption. Next we apply this optimization framework on top of a prediction based DPM policy to develop a new fuel-efficient DPM scheme. The proposed algorithm was applied to a real trace based MPEG encoding example and demonstrated up to 32% more system lifetime extension compared to a competing scheme.