A novel metal–organic framework [Cd₃(CPEIP)₂(DMF)₃]·solvent (1) based on a neutral non-oxo triangular [Cd₃(COO)₆] secondary building unit (SBU), was synthesized under solvothermal conditions by using a rigid unsymmetrical tricarboxylate ligand 5-((4-carboxyphenyl)ethynyl)isophthalic acid (H₃CPEIP). Single-crystal X-ray diffraction analysis reveals that compound 1 crystallizes in the monoclinic space group C2/c. The crystal structure exhibits a rare (3,3,6)-connected three-dimensional (3-D) framework with vertex symbol of (4².6)(4³)(4⁵.6⁴.8⁶). The incorporation of CPEIP³⁺ into 1 gives rise to high luminescence in solid state. The emission of micrometer-sized compound 1 (1′) dispersed in ethanol could be quenched efficiently by picric acid (PA), indicating that this compound could be utilized as a chemosensor for detection of aromatic explosives.