The element-free spline method is proposed to analyze the vibration of the functionally graded material (FGM) plate with various boundaries. The field functions are constructed by using the linear combination of double B-spline basis functions together with mixed displacement parameters and then an equation based on Reddy's third order plate theory is developed for the vibration analysis of the FGM plate. The validity of the proposed method is illustrated by some numerical examples. Six lower vibration frequencies of FGM plate are calculated under various boundaries and the influence of boundary condition and material gradient on vibration frequencies are also discussed. The proposed method needs less computational cost and has high accuracy.