Although bimetallic nickel-cobalt sulfides (Ni/Co-S) have shown promising candidates as pseudocapacitive materials with excellent electrochemical performance, achieving high energy density, high power density, and good cyclability of Ni/Co-S electrode remains a challenge. In this study, the graphene foam (GF) with a three-dimensional (3D) skeleton was successfully prepared using a chemical vapor deposition (CVD) method. Subsequently, Ni/Co-S was in situ grown on the GF through a two-step hydrothermal method. A series of Ni/Co-S@GF-x (x=1, 2, 3) electrodes were prepared and optimized for electrochemical performance by regulating the molar ratio of Ni/Co salt precursors (3:1, 4:1, 5:1). The abundant pore structure of Ni/Co-S@GF not only facilitates ion migration, but also provides numerous electrochemical redox active sites for reactions. When utilized as electrodes in supercapacitors, the Ni/Co-S@GF-2 with a Ni/Co salt’s molar ratio of 4:1 displays a specific capacity of 4.68 C cm−2 at 1 mA cm−2. Furthermore, an asymmetric supercapacitor (ASC) was assembled using the optimal Ni/Co-S@GF-2 as cathode and Walnut shell-derived porous carbon as anode to evaluate the actual energy storage characteristics of the device. The ASC delivers a high power density of 822.86 mW cm−2 at an energy density of 32.0 mWh cm−2. This work presents a promising approach for designing and preparing nickel-cobalt sulfides for application in flexible energy storage devices.