The energy management (EM) and driving speed co-optimization of a series hybrid electric vehicle (S-HEV) for minimizing fuel consumption is addressed in this article on the basis of a suitably modeled series powertrain architecture. The paper proposes a novel strategy that finds the optimal driving speed simultaneously with the energy source power split for the drive mission specified in terms of the road geometry and travel time. Such a combined optimization task is formulated as an optimal control problem that is solved by an indirect optimal control method, based on Pontryagin's minimum principle. The optimization scheme is tested under a rural drive mission by extensive comparisons with conventional methods that deal with either speed optimization only or EM strategies with given driving cycles. The comparative results show the superior performance of the proposed method and provide further insight into efficient driving.