Asymmetric supercapacitors provide a promising approach to fabricate capacitive energy storage devices with high energy and power densities. In this work, asymmetric supercapacitors with excellent performance have been fabricated using ternary (Ni, Co)0.85Se on carbon fabric as binder-free positive electrode and porous free-standing graphene film as negative electrode. Owing to their metal-like conductivity (~1.67×106 Sm−1), significant electrochemical activity, and superhydrophilic nature, our nanostructured ternary nickel cobalt selenides result in a much higher areal capacitance (2.33Fcm−2 at 4mAcm−2), better rate performance and cycling stability than their binary selenide equivalents, and other ternary oxides and chalcogenides. Those hybrid supercapacitors can afford impressive areal capacitance and stack capacitance of 529.3mFcm−2 and 6330mFcm−3 at 1mAcm−2, respectively. More impressively, our optimized asymmetric device operating at 1.8V delivers a very high stack energy density of 2.85mWhcm−3 at a stack power density of 10.76mWcm−3, as well as 85% capacitance retention after 10,000 continuous charge–discharge cycles. Even at a high stack power density of 1173mWcm−3, this device still deliveries a stack energy density of 1.19mWhcm−3, superior to most of the reported supercapacitors.