Two Co(II) metal-organic frameworks (Co-MOFs), namely, [Co(DMTDC)(bimb)]n (Co-MOF-1) and {[Co(DPTDC)(bimb)(H2O)]·2DMF}n (Co-MOF-2) (H2DMTDC = 3,4-dimethylthieno[2,3-b]thiophene-2,5-dicarboxylic acid, H2DPTDC = 3,4-diphenylthieno[2,3-b]thiophene-2,5-dicarboxylic acid, bimb = 1,4-bis((1H-imidazol-1-yl)methyl)benzene), were obtained by the reaction of flexible N-containing ligand bimb and two structurally related thiophene-containing ligands H2DMTDC and H2DPTDC, respectively. These Co-MOFs displayed a 3D framework and porous structure, respectively. Co-MOF-1 and the activated sample Co-MOF-2' could act as green heterogeneous catalysts for the one-pot multicomponent Biginelli reaction, specifically the dehydration condensation process involving aldehydes, acetoacetates, and urea to yield dihydropyrimidin-2(1H)-ones. The reaction has advantages such as solvent-free conditions, water as only byproduct, readily accessible starting materials, excellent functional group compatibility, and simple operation. Both catalysts exhibited a wide substrate scope and maintained significant catalytic activity over five cycles. The special catalytic performance may be ascribed to functional groups within the ligand.