Two nickel metal-organic frameworks (Ni-MOFs) based on a nitrogen-containing rigid tetracarboxylic acid ligand had been synthesized by the hydrothermal method, namely {[Ni(H4L1)0.5(4,4′-bibp) (H2O)]·1.5H2O}n (1) and {[Ni(H4L1)(H2O)2]·H2O}n (2) (H4L1 = 5,5′-(1H-1,2,4-triazole-3,5-diyl)diisophthalic acid, 4,4′-bibp = 4,4′-di (1H-imidazol-1-yl)-1,1′-biphenyl). Crystal structure analysis revealed that the two complexes exhibited varied structures in the presence or absence of the auxiliary N-donor ligand 4,4′-bibp: the complex 1 was a three-dimensional (3D) metal-organic framework with a (1,2,4,5)-connected {4.64.8}2{42.64}3{6}2 topology. In the complex 2, the carboxylate ligand was used as a junction point to form a 2D layered structure with Ni(II). The results showed that the addition of the 4,4′-bibp has a very important effect on the structure of the complexes. Some conventional characterizations were carried out, such as: Infrared (IR) spectroscopy, powder X-ray diffraction (PXRD) and thermogravimetric (TGA) analyses. Moreover, the ORCA program was used to perform density functional theory (DFT) calculations to investigate the molecular properties of the two complexes.