Herein, hybrid micro-supercapacitors (MSCs), consisting of positive CoNi layer double hydroxides (LDHs) decorated on carbon nanotubes (CoNi LDHs@CNTs) and negative CNT electrodes, were assembled by facile drop-coated and electrodeposition methods. The as-fabricated MSCs were optimized in view of electrochemical performance, and the CoNi LDHs-2@CNTs//CNT MSC exhibited a favorable performance and was thus chosen to be the candidate for MSC device package. The packaged CoNi LDHs-2@CNTs//CNT MSC demonstrated a large areal capacitance of 11.0 mF·cm–2 at a current density of 0.08 mA·cm–2, a good rate performance (56% areal capacitance retained at a higher current density of 0.4 mA·cm–2), and a favorable cycling stability and reversibility (92% of the original areal capacitance was retained after 5000 cycles). Furthermore, the MSC device recorded an energy density of 1.5 μWh·cm–2 at a power density of 42.5 μW·cm–2 and was successfully applied for the storage of energy supplied by solar cells to operate a red light-emitting diode. All these findings demonstrated the promising practical energy storage application of the as-fabricated hybrid MSC devices in the construction of sunlight-powered energy storage systems.