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This paper studies vibration of sandwich beams reinforced by carbon nanotubes (CNTs) under a moving point load. The core of the beams is homogeneous while their two faces are of carbon nanotube reinforced composite material. The effective properties of two face sheets are determined by extended rule of mixture.  A uniform distribution (UD) and four different types of functionally graded (FG) distributions, namely FG-X, FG-FG-V, FG-O, are considered. Based on a third-order shear deformation theory, a finite element formulation is derived and used to compute the vibration characteristics of the beams.