Abstract: The governing equations of ground-beam based on the theory of fractional derivative and viscoelastic theory was given.The analytical solution was obtained by the properties of fractional derivative.The influences of the exponent number of fractional operator and modulus ratio of ground and beam on displacements and time varying rule of displacement were investigated.Results indicated that exponent number of fractional operator and modulus ratio had great influences on the displacement of groud-beam.Classical viscoelastic model can't reflect the long-term effects of the deformation of ground beam.