Abstract: A size-dependent model for the free vibration of plane orthotropic functionally graded micro-beams was developed on the basis of a new modified couple stress theory. The model contains two material length scale parameters, which enables it to separately represent the different scale effects in two orthogonal directions. The present model can be degenerated to classical macroscopic model when the geometrical size of the beam is much larger than the material length parameter. The governing equations were derived through Hamilton's principle. A simply supported micro-beam was taken as the illustrative example and analytical solved. The influences of geometrical size and power law index on the scale effects were analyzed. Numerical results indicate that the natural frequencies of the micro-beam predicted by the present model are always greater than those predicted by the classical FG beam model, i.e. the scale effects are captured. The scale effects will be gradually weaken with the increasing of the geometrical size of the beam, and diminish when the geometrical size is much larger than the material length parameter. The scale effects reflected by higher order natural frequencies are more apparent than that reflected by lower order natural frequencies. In addition, the power law index also has a specific influence on the scale effects.