To improve the reliability of numerical-controlled machine tool, the reliability and sensitivity of static stiffness of single nut ball screw pair were studied. Based on the Hertz Contact Theory, a model of axial contact deformation was established using the lead, contact angle, nominal diameter of ball screw, raceway curvature ratio, working load and other technical parameters of single nut ball screw pair. According to the principle that the inaccuracy of axial contact deformation for nut ball screw pair is less than the machining accuracy, a nut ball screw pair reliability model was established. The reliability and sensitivity of single nut ball screw pair were analyzed and calculated using the modified first order second moment method. The results show that the static stiffness of nut ball screw pair can be improved by increasing the lead of nut ball screw and decreasing the raceway curvature ratio appropriately, and the reliability of nut ball screw pair can be improved by decreasing the working load to reduce axial contact deformation of nut ball screw pair.