Supercapacitors have a wide range of potential applications in new energy storage and electric cars due to their high capacity, high power density, and extended cycle life, and the electrode materials are a key to enhancing the supercapacitor performance. NiCoMnSe electrode materials were prepared by a simple low-temperature hydrothermal reaction method and a heat-treatment selenization method using ZIF-67 as a template. The optimum electrochemical performance was obtained via adding carbon nanotube (CNT) or graphene oxide (GO) to the ZIF-67 template. The results show that the optimum NiCoMnSe/CNT electrode has a specific capacitance of 624.0 F/g at 1 A/g and a multiplicative performance of 90.1% at 10 A/g. The capacity retention rate is 88% at 15 A/g for 1 000 cycles. This superior capacitive performance is attributed to the presence of CNT introducing additional mesopores around NiCoMnSe, thus enhancing the contact between the electrolyte and the active material. The NiCoMnSe/CNT/activated carbon device exhibits a high energy density (43.3 W·h/kg) at a power density of 800 W/kg and a good capacity retention (i.e., 91.4% after 1 000 cycles) due to the asymmetric nature of the supercapacitor.