Many of the studies have been developed earlier for describing High Tc superconductivity of oxides in YBCO material which has optimally a phase transition temperature of92K. The main aim of this graduate project work is to present the change in superconductivity properties when applying the magnetic field and varying oxygen contents in YBa2Cu307_x· The crystal structure and superconductivity properties change with oxygen content in the range 0.05 ~ x~ 0.56. The lattice parameter and unit cell of volume changes with oxygen concentration as well. All the sample of YBCO in this range has orthorhombic structure. The superconductivity properties such as transition temperature, electric current density, V-I characteristic, Resistance-Temperature Measurements, magnetic levitation force of YBCO are also described. Keywords: YBCO, Crystal structure, Penetration depth, Coherence length, Critical magnetic field.