A new metal–organic framework {(Me2NH2)2Co3(μ3-O)­(btb)2(py)­(H2O)·(DMF)2(H2O)2}n (Cobtbpy) was solvothermal synthesized (H3btb = 1,3,5-tri­(4-carboxylphenyl)­benzene, py = pyridine, DMF = N,N-dimethylformamide). Cobtbpy shows a (3,6)-connected rtl 3D network with a point symbol of (4·62)2(42·610·83) based on the Co3(μ3-O) clusters. The obtained Cobtbpy has stable, accessible, dense active sites and can be applied in the potassium- and sodium-ion batteries. Through mixing with single-walled carbon nanotubes, the prepared composite anode material Cobtbpy-0.9 achieved a high reversible capability, delivering 416 mAh/g in the potassium-ion batteries and 379 mAh/g in the sodium-ion batteries at 0.05 A/g. The outstanding properties of Cobtbpy-0.9 in the batteries demonstrated that this MOFs-based carbon composite is a highly desirable electrode material candidate for high-performance potassium- and sodium-ion batteries.