In this study, based on the anisotropic modified couple stress theory, a free vibration model of composite laminated Reddy plate containing only one internal material length scale parameter was developed. The presented model predicted the frequency of free vibration of composite laminated plate in micro scale more accurately than the Kirchhoff model in published literature. The Hamilton's principle was employed to derive the governing equations of motion and the boundary conditions. A simply supported square plate was taken as an illustrative example, the problem of which was solved analytically. Influence of the length scale parameter on natural frequency of material was analyzed, and differences between the results obtained using the Kirchhoff, Mindlin and Reddy plate theories were discussed. Numerical results showed that the presented model was capable of capturing the scale effects. The natural frequencies were always shown to be overestimated by the Kirchhoff theory, especially in thick plate cases, when comparing with the more accurate results obtained using the Mindlin or Reddy theory.