In recent years, there has been an increasing need for rechargeable energy-storage devices of many kinds. There are some applications for which energy density is important, whereas for others rate capability (high-power density) and prolonged durability are essential. Batteries address the need for high energy density, while electrochemical capacitors, so called, supercapacitors, can be relevant for the high power density purpose. In between these two kinds of devices, it is possible to develop hybrid systems which possess intermediate properties between supercapacitors and batteries, and which contain both a capacitive or pseudocapacitive electrode and a battery type electrode. With a good selection of electrodes, it is possible to achieve high-rate capability and durability, and also enhanced specific energy density compare to standard supercapacitors. This paper describes the development and study of Li-ion-based hybrid capacitor based on a carbon-based capacitive negative electrode, LiMn2O4 spinel as positive electrode and aqueous solutions with Li2SO4 salt as the electrolyte (pH = 7.5). Here, we demonstrate full hybrid devices as a proof of concept.