Recently synthesized double perovskite Bi₂NiCrO₆ with Fm-3m structure is investigated with density functional theory calculation using FP-LAPW approach to evaluate its electronic and magnetic properties. The calculation used the Hubbard U parameter (U_eff = 5eV) to account for the localized nature of 3d orbitals that GGA cannot predict correctly. The compound is found to have a Ferromagnetic ground state, and the energy band gap observed in spin up channel and metallic in spin down channel suggests a half-metallic nature with total magnetic moment of 4 μ_B per atomic unit. Further, we studied by substituting a series of 3d elements on Ni and Cr sites on the parent material. Replacing Cr site in the parent compound with Ti, Mn, or Ni, the band gap opening in both spin channels is observed, making them semi-conductors with the energy band gap of 0.581 eV, 0.839 eV, and 0.556 eV respectively. Whereas Cr site was replaced with Co and Zn, half-metallic behavior is observed with a majority contribution of Co-t_2g and Zn-e_g orbitals respectively, in the Fermi level. On substituting Ni site with Mn, Fe, Cu, and Zn are also showed half-metallic behavior with the majority contribution of Cr-t_2g orbitals in the Fermi level. Few of these substituted compounds show ferromagnetic to ferrimagnetic ground state transition. These half-metallic compounds can be good candidates for spintronic devices, and semi-conducting compounds can be good candidates for thermal transistors and phototransistors.