Bimetallic metal-organic framework (MOF) has attracted great interest as an electrode for supercapacitors. Most metal sources are limited to valences of + 2 and + 3. We select metal sources of Co (II) and Mo (VI) and demonstrated a crystalline bimetallic MOF precursor prepared by using a facile chemical synthesis. The one-step solvothermal strategy is assisted by thioacetamide (TAA) for the self-assembly Co-Mo-S nanosheet arrays (Co-Mo-S NSAs). TAA-induced etching is essential to regulate the assembly of amorphous structures. Otherwise, only a single-structure crystalline Co-Mo-S could be obtained. The Co-Mo-S NSAs show a large specific capacitance of 1805.28 F g−1 at a current density of 0.5 A g−1. A Co-Mo-S NSAs//AC battery−supercapacitor hybrid (BSH) make with activated carbon as the negative electrode and Co-Mo-S NSAs as the positive electrode. At a current density of 0.5 A g−1, the BSH shows a high energy density of 169.73 Wh kg−1 and a power density of 371.44 W kg−1. After 50,000 cycles, the capacitance retention rate is as high as 94.44%, showing good reversibility and cycle life. This work provides an effective strategy for manufacturing bimetallic MOF-based metal sulfide heterostructure electrode materials for practical energy storage and conversion.