A novel hydrogen-bonded metal-organic framework (H-MOF) [Co(HL)2](DMF)1.2(H2O)2.4 (1·solv), in which L = 2,2':6',2''-terpyridine-5,5"-diyl biscarboxylate, was prepared. An intermolecular single H-bond between carboxy and carboxylate sites was present in this compound. The crystal structure of 1·solv showed a 4-fold interpenetrating H-bonded diamond framework. After the desorption of the crystal solvents, 1·desolv exhibited normal and reverse spin-crossover (SCO) behaviours, providing an asymmetric thermal hysteresis loop.