MR characteristics of $Al_2$ $O_3$ based magnetic tunneling juction with various $Al_2$ $O_3$ thicknesses were investigated. Spin-dependent tunneling junctions, in which the tunneling barrier $Al_2$ $O_3$ is formed by depositing a 1-3 nm thick Al layer, followed by thermal oxidation at room temperature in an $O_2$atmosphere, were fabricated on 4$^{circ}$tilt(111)Si substrate in 3-gun magnetron sputtering system. The top and bottom ferromagnetic electrodes were Ni$_{80}$Fe$_{20}$ and Co. A maximum Tunneling MR ratio of 14% was obtained in the junction of which insulating barrier thickness was 2 nm. By increasing the tunneling voltage across the junction, maximum MR ratio reduced and finally showed no MR characteristics.s.