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This paper uses a new refined beam theory based on neutral surface position for the static and free vibration analysis of functionally graded material beams. The theory accounts for parabolic distribution of the transverse shear strains and satisfies the zero traction boundary conditions on the surfaces of the beam without using shear correction factors. The neutral surface position for a functionally graded beam with its material properties varying in the thickness direction is determined. Based on the present refined shear deformation beam theory and the neutral surface concept, the equations of motion are derived from Hamilton's principle. A static and free vibration frequency is given for different material properties. The accuracy of the present solutions is verified by comparing the obtained results with the existing solutions.