According to the first order slip velocity boundary, a modified Reynolds equation for micro gas journal bearings is presented with consideration of effective viscosity under a rarefied flow condition. A modified Reynolds equation is attained and solved using the finite difference method. The nondimensional pressure, load capacity, and attitude angle for micro gas journal bearings under different reference Knudsen numbers (the ratio of ambient molecular mean free path to the average radial clearance), bearing numbers, and eccentricity ratios are obtained. The numerical analysis demonstrates that the slip model with effective viscosity is in a better agreement with the FK model derived by Fukui and Kaneko than that without effective viscosity. When the bearing number is constant, the pressure and load capacity decrease, and the attitude angle changes inversely with the increasing reference Knudsen number. The larger the eccentricity ratio, the larger change in attitude angle from effective viscosity. When eccentricity ratio is less than 0.6, the attitude angle changes softly, and the effect of effective viscosity is unobvious. When the eccentricity ratio is constant, the influence of effective viscosity on nondimensional load capacity and attitude angle becomes larger with the increasing bearing number, and the influence is more prominent with a larger reference Knudsen number.