A single-phase Sr2CuO3+δ superconductor is synthesized under high temperature and high pressure, in which oxygen atoms only partially occupy the apical sites next to the CuO2 planes and act as hole-dopants. The superconducting transition temperature with Tcmax = 75 K is achieved in the material. Structure analysis from x-ray powder diffraction data show that this material crystallizes into a K2NiF4 structure with tetragonal unit cell of α = 3.795(3) (A) and c = 12.507(1) (A). Energy-dispersive synchrotron x-ray-diffraction studies at ambient are performed on powder samples of St2CuO3+δ in a diamond-anvil cell at pressure up to 35 GPa. Anisotropic compressibility is found. Pressure-induced isostructural phase transition might exist as revealed by the discontinuous change of crystal cell volume V with pressure.