Abstract: In the case of a sparse grid, when the displacement element is used to analyze the vibration of a stiffened plate, the stiffness of the model is relatively hard, so there will be a larger error in the natural frequency obtained from the model. In this paper, the generalized mixed variational principle for vibration characteristics of the structure is proposed. On this basis, the undamped free vibration characteristic equation of the hexahedral non-conforming generalized mixed element is established. Theoretically, the stiffness matrix of the non-conforming generalized mixed element is softer than that of the non-conforming displacement element, so the numerical results will be closer to the real solution of the actual structure. Numerical example shows that the natural frequency obtained from the non-conforming generalized mixed element model is more accurate with the same finite element model. On the other hand, the consistency of the natural modes between the non-conforming generalized mixed element model and the non-conforming displacement element further proves the reliability of the method in this paper.