The governing differential equations for axially moving Timoshenko beam made of functionally graded material are obtained based on the Hamilton principle. A single fourth-order partial differential equation is derived by introducing a new unknown function. For simply supported FGM Timoshenko beam, the characteristic equation is obtained by using WDQ method, and the relation of the first three orders complex frequencies of the beam with axial movement speed are given. The form of instability of the FGM Timoshenko beam in different value of axial movement speed is analyzed in detail, and compared with that of the homogeneous material beam. The effects of length-to-height ratios and gradient index on the stability of the FGM Timoshenko beam are discussed.