The generalized differential quadrature method (GDQM) developed recently is more and more widely used in structural analysis, but that is restricted by some conditions. The finite element method (FEM) is a conventional numerical method, but the calculational work is very great. In this paper, the GDQM and the FEM are combined together to analyze the transverse vibration of circular plates with an elastically mounted mass. The results show that this combination is a new way first proposed in this paper to solve the problems with complex domains in structural analysis. And it is a rapid, efficient, accurate and flexible numerical method with both the advantages of the GDQM and the FEM. Comparison with the existing literature has proved that the results obtained by this method are very accurate.