The effect of the mass damper on the fundamental frequency reduction of the functionally graded material (FGM) beam is investigated. Mori–Tanaka homogenization scheme is used to model through-the-thickness material gradation. The various classical boundary conditions, including simply supported beam, clamped beam, pinned-clamped beam and cantilever beam as well as shear hinge end condition are considered. It is assumed that the lumped mass damper is connected to the beam at an arbitrary position without sliding. The total potential energy is minimized by employing spectral Ritz method to calculate fundamental frequency and corresponding mode shape. The reduction of the frequencies in the presence of the attached lumped mass damper is observed. The dimensionless frequency reduction is affected by lumped mass amount and position. The lumped mass position plays an important role for vibration control of the beam.