The direct parallel connection of a high energy Li-ion battery (MP 176065 Integration, Saft SA, France) and a supercapacitor (BCAP0310 P250, Maxwell Technologies Inc., Switzerland) was simulated using an available battery model in MATLAB/Simulink for various ratios of capacitor to battery energy content. The Ragone plots for the different combinations were calculated for constant power and pulsed power discharge, respectively. The Ragone plot of the hybrid device for constant power discharge shows an improved performance with respect to the capacitor in terms of available specific energy and an improved performance with respect to the battery in terms of available specific power. However, the combined device never meets the specific performance of the battery at high specific energy or of the supercapacitor at high specific power. For a pulsed discharge, however, the Ragone plots of the combined device show that the performance extends into an energy–power regime inaccessible to the single devices. The improved performance depends on the duty cycle of the pulse pattern and on the relative energy under each pulse.