Rotating annular plates have many important applications in various parts of industry. Free vibration analysis of rotating annular plates can help in engineering designing annular plates. Circular saw, CD, DVD and hard disk are some examples of parts of annular plates that used in daily usage. By building these plates from Functionally Graded Materials (FGM), we can extract more capability from them. FGMs are composite materials that change one or more properties continuously in one or multi directions. This property gives so many ability and flexibility to designers and manufacturers in the field of making parts that must endure hard conditions of environment or loads. We study free vibration of rotating FGM annular plate with angular acceleration. Governing relations come from classical plate theory. Equations of motion in cylindrical coordinates are derived by using free body diagram. Equations of motion in radial and tangential directions are solved by differential quadrature method and the results are used as coefficients for transverse motion equation. Transverse motion equation is discretized by using differential quadrature method and then is solved. Dimensionless natural frequencies that have influence on the amplitude of vibration in addition to fundamental frequency are complex. Numerical results are derived for combination of two boundary conditions: clamped and simply supported. Influence of variation of: angular acceleration function, radial graded indice, thickness and inner radius-to-outer radius ratio of annular plate over amplitude and frequency are shown. Angular acceleration cause changes in tangential displacement of annular plate and angular velocity changes radial displacement value of plate instead. Results show that in general, for all of boundary condition types, amplitude of annular plate for positive (or negative) angular acceleration by passing time decrease (increase). This result has no difference for changing of other variables like: thickness, inner radius-to-outer radius and radial graded indice. All of diagrams for both amplitude and frequency measured by dimensionless time and dimensionless natural frequency. Although, our result only include dimensionless parameters, but it shows behavior of plate properly and give a good guide for design and building annular plate with desired ability for enduring hard conditions. Key Words: Free Vibration, Rotating Annular Plate, Functionally Graded Material, Angular Acceleration, Dimensionless Natural Frequency.