Encapsulating transition metals or oxides in N-doped carbonaceous materials is a desirable strategy in the design of advanced energy materials in confined spaces. In this study, a core@shell structure of Co–Co3O4 core particles enclosed in a shell of carbon-nanotube (CNT)-incorporated nitrogen-doped carbon (hereafter abbreviated as Co–Co3O4@CNT–NC) was synthesized via simple pyrolysis of a melamine–formaldehyde (MF) resin and cobalt acetate composite in a N2 atmosphere, followed by oxidation with H2O2. Because of the intimate contact between the Co–Co3O4 core particles and the graphitic shells, the obtained samples showed excellent performance. The as-prepared Co–Co3O4@CNT–NC structure exhibited improved electrical conductivity, which is suitable for an electrode material in electrochemical capacitors. It can deliver a high specific capacitance of 823.4 F g−1 at a current density of 1 A g−1, as well as a capacitance retention of 93.6% after 10000 cycles. Moreover, an asymmetric two-cell supercapacitor composed of a Co–Co3O4@CNT–NC positive electrode and a reduced-graphene-oxide negative electrode exhibited a high energy density of 46.7 Wh kg−1 at 1601.1 W kg−1. The easy preparation and high performance of the Co–Co3O4@CNT–NC composite make it an excellent material for supercapacitors application.