A high performance asymmetric supercapacitor (ASC) has been fabricated by using nickel oxide-cobalt oxide nanosheets (NiO–CoO NSs), which were directly grown on carbon nanotubes (CNTs) and hydrothermal carbon spheres (HTCs) as positive and negative electrodes, respectively. Both electrode materials are binder-free prepared by using a catalytic chemical vapour deposition (CVD) approach followed by a facile hydrothermal method for cathode and a one-step environmental-friendly route called hydrothermal carbonization for anode. Using NiO–CoO NSs@CNTs and HTCs, which were directly grown on Ni foam, not only leads to a very small equivalent series resistance, but also provides an impressive capacitive performance. The assembled ASC exhibits remarkable capacitive performance over a broad operational potential window ensuring outstanding energy densities (84.625 Wh. kg−1 at 3 A g−1). Other noteworthy features of the prepared supercapacitor include its superior power density (7810 W kg−1 at 9.5 A g−1) and cycling stability with capacitance retention almost over 80% after 6000 cycles. These electrochemical results point to NiO–CoO NSs@CNTs-Ni//HTCs-Ni based asymmetric supercapacitors as a promising remedy for energy crisis and environmental deterioration problems.