A new 3D terbium(III) metal-organic network [Tb(HIMDC)(HCOO)(H₂O)]_n (complex 1) has been synthesized by Tb³⁺ ions coordinated with 4,5-imidazole dicarboxylic acid (H₃IMDC) and formic acid under solvothermal conditions with the mixed solvents of N,N-dimethylformamide (DMF) and H₂O. The unambiguous structural determination has been confirmed by single-crystal X-ray diffraction combined with elemental analysis, infrared (IR) spectrum, thermogravimetric analysis (TGA) and powder X-ray diffraction (PXRD). Complex 1 crystallizes in orthorhombic Fdd2 space group with a = 22.295(2), b = 24.097(3), c = 6.7256(6) Å, V = 3613.3 ų, Z = 16, D_c = 2.765 g/cm³, F(000) = 2816, μ = 7.855 mm^-1, the final R = 0.0173 (I ≥ 2σ(I)), wR = 0.0416 (all data) and GOOF = 1.068. In complex 1, the Tb³⁺ ions are connected by HIMDC^2- anions into 2D metal-organic layers which are further extended into a three-dimensional (3D) architecture through formic acid functional motif. In addition, complex 1 shows intense and characteristic green luminescence.