Abstract: A contraction design was conducted for axis-symmetric nozzles in hypersonic wind tunnel. The influence of arc length and curvature radius on the transonic throat flow and nozzle outlet flow was studied by constructing an AQA curve. Two new contraction curves were proposed on the basis of trigonometric function, hyperbolic function, and B-spline function. The curvature radius at the entrance and exit of the contraction can be adjusted by using these two types of curves. CFD solutions were computed to determine the influence of the throat curvature radius on the flow at the exit of a Cresci nozzle and a Sivells nozzle. The results indicate that continuous throat curvature radius is critical for the consistence between real nozzle flow and designed flow. When the continuity of curvature radius cannot be guaranteed at a throat, the upstream curvature radius of the throat is needed to be larger than the downstream one.