SmBa₂Cu₃O_7-δ (SBCO) superconductor is synthesized through the solid state reaction method and also the alumina (γ-Al₂O₃) nanoparticles with the average size of 70 nm were made through the sol-gel self-combustion method and they were compared with the SIGMA Al₂O₃ nanoparticles. Then the SBCO superconductor was doped with different percentage of the alumina nanoparticles and its properties were studied and also the oxygen content of the samples was measured by iodometric titration. It was found that the oxygen content and critical temperature of the doped samples reduced. The study of resistivity versus temperature of the samples showed a semiconducting behavior in the normal state; i.e. by increasing the temperature, the resistivity decreased. The critical current density of 0.1 percent doped sample increased significantly, but it decreased by further doping. X-ray diffraction patterns of the doped samples showed that the alumina nanoparticles did not inter into the crystal structure of the superconductor. Also, a few peaks of the X-ray diffraction patterns of the doped samples were absent and the width of the peaks was broadened compared with the undoped sample. SEM images showed that the alumina nanoparticles spread on the surface of the grains and boundaries of the doped samples.