In this paper, the resonance vibration of the boiler-supporting frame structure and the boiler is analyzed. The natural vibration period is solved by using subspace iteration method in finite element software ANSYS. A couple of conclusions are obtained and can be referred for structural design of the boiler-supporting frame structure. The first conclusion is that the result obtained with Finite Element Method is approximate to the actual measurement. In order to ensure the reliability of the theoretical calculation, FEM should be adopted in the calculation of similar structure as the boiler-supporting frame. The second conclusion is that the fore several order vibration frequencies of the boiler-supporting frame are approximate to the working frequency of the boiler. Consequently, the resonance vibration is apt to occur. So in order to avoid resonance vibration with the boiler, natural vibration period of the boiler-supporting frame structure should be analyzed in the design of the structure.