Due to non-linear factors such as the rate capacity and the recovery effect, the shape of the battery discharge curve plays a significant role in the overall lifetime of the batteries. Accordingly, this paper proposes a simple heuristic battery-aware speed scheduling policy for periodic and non-periodic real-time tasks in Dynamic Voltage Scaling (DVS) systems with non-negligible leakage/static power. A set of comprehensive analysis has been conducted to compare the battery efficiency of the proposed policies with an optimal solution, which could be derived via the Calculus of Variations (CoV). These evaluations have taken into account both periodic and non-periodic tasks in DVS-based systems. Our experiments have shown a maximum of 7% difference between the optimal solution and the simple heuristic speed scheduling for realistic settings of the battery model. By considering the calculated optimal speed scheduling for different tasks (with different utilizations), a two-phase algorithm has been proposed, in which a speed approximation function is being calculated offline based on curve fitting, while the best execution speed is applied online. The results show a maximum of 17.7% and 11.3% battery charge saving for non-periodic and periodic tasks in comparison to the baseline critical frequency method, respectively.