The vibrations and stability are investigated for an axially moving rectangular antisymmetric cross-ply composite plate supported on simple supports. The partial differential equations governing the in-plane and out-of-plane displacements are derived by the balance of linear momentum. The natural frequencies for the in-plane and out-of-plane vibrations are calculated by both the Galerkin method and differential quadrature method. It can be found that natural frequencies of the in-plane vibrations are much higher than those in the out-of-plane case, which makes considering out-of-plane vibrations only is reasonable. The instability caused by divergence and flutter is discussed by studying the complex natural frequencies for constant axial moving velocity. For the axially accelerating composite plate, the principal parametric and combination resonances are investigated by the method of multiple scales. The instability regions are discussed in the excitation frequency and excitation amplitude plane. Finally, the axial velocity at which the instability region reaches minimum is detected.