The maximum capacitive potential window of certain pseudocapacitive materials cannot be accessed in aqueous electrolytes owing to the low dissociation potential of 1.2 V possessed by water molecules. However, the inferior pseudocapacitance exhibited by the commonly used electrode materials when integrated with non-aqueous electrolytes still remains a challenge in the development of supercapacitors (SC). Proper selection of materials for the electrode and a rational design process are indeed important to overcome these practical intricacies so that such systems can perform well with non-aqueous electrolytes. We address this challenge by fabricating a prototype all-solid-state device designed with high-capacitive V2O5 as the electrode material along with a Li-ion conducting organic electrolyte. V2O5 is synthesized on a pre-treated carbon-fibre paper by adopting an electrochemical deposition technique that effects an improved contact resistance. A judicious electrode preparation strategy makes it possible to overcome the constraints of the low ionic and electrical conductivities imposed by the electrolyte and electrode material, respectively. The device, assembled in a symmetrical fashion, achieves a high specific capacitance of 406 F g-1 (at 1 A g-1). The profitable aspect of using an organic electrolyte is also demonstrated with an asymmetric configuration by using activated carbon as the positive and V2O5 as the negative electrode materials, respectively. The asymmetric device displays a wide working-voltage window of 2.8 V and delivers a high energy density of 102.68 W h kg-1 at a power density of 1.49 kW kg-1. Moreover, the low equivalent series resistance of 9.9 Ω and negligible charge transfer resistance are observed in the impedance spectra, which is a key factor that accounts for such an exemplary performance.