Superconductivity through Hubbard model has been studied following Hartree FockrnApproximation. The theoretical study has been made on the origin of superconductivityrnin electron-electron interaction with coulomb repulsion which is not phononic.rnThe former interaction is under some condition, qualitatively different as comparedrnto the latter interaction . The study by considering a Hubbard model is focused andrnbrought out by applying the canonical transformation method as well as by simplernrenormalization operation that excludes double occupancy in the effective HubbardrnHamiltonian of the system and goes over in to the t-J model Hamiltonian that servesrnas a reference point (fixed point ). For small deviations from half filling holes move inrnthe antiferromagnetic lattice and create disorder and establishes superconductivity.rnThis Hamiltonian is used and theoretically examined in the second quantization notationrnby using Greenâ€™s function formalism and suitable decoupling approximationsrnthe survival of superconductivity has been shown with the computation of supperrnconducting order parameter ( ) and transition temperature (Tc) mathematically tornmake known its possibility. The phase diagram of the numerical estimates of thernsuperconducting transition temperature versus values of electron (hole) boson couplingrnconstant has been obtained and it is in agreement with the the experimentalrnobservation. We found that supper conductivity is obtained through Hubbard model