Based on the von Karman plate theory, the transverse vibration equation of a spinning thin axisymmetric annular plate with clamped inner-boundary and free outer-boundary was formulated. The discretization of a simplified partial differential equation was obtained by the Galerkin method. For any nodal diameter , the smallest eigenvalue (zero nodal circle) of a stiffness operator and the eigenfrequency of the corresponding mode with regard to the simplified equation were calculated. The calculating method for the critical speed was given, and the critical speed versus inner-to-outer radius ratio and Poisson’s ratio was investigated. The analysis results indicate that there is no critical speed for nodal diameter and ,but for other nodal diameter , the critical speed increases with the increase of the inner-to-outer radius ratio and decreases with the increase of the Poisson’s ratio. These observation is helpful to the design of annular plate for high-speed applications such as computer hard disks ,circular sows ,and turbines.