We suggest that a family of Ni-based compounds, which contain [Ni2M2O] 2− (M=chalcogen) layers with an antiperovskite structure constructed by mixed-anion Ni complexes, NiM4O2, can be potential high temperature superconductors upon doping or applying pressure. The layer structures have been formed in many other transitional metal compounds such as La2B2Se2O3(B=Mn, Fe,Co). For the Ni-based compounds, we predict that the parental compounds host collinear antiferromagnetic states similar to those in the iron-based high temperature superconductors. The electronic physics near Fermi energy is controlled by two eg d-orbitals with completely independent in-plane kinematics. We predict that the superconductivity in this family is characterized by strong competition between extended s-wave and d-wave pairing symmetries.