Abstract In this paper, a highly accurate and rapidly converging hybrid approach is presented for the Quadrature Element Method (QEM) solution of plate free vibration problems. The hybrid QEM essentially consists of a collocation method in conjunction with a Galerkin finite element technique, to combine the high accuracy of the Differential Quadrature Method (DQM) for the efficient solution of differential equations with the generality of the finite element formulation. This results in superior accuracy with fewer degrees of freedom than conventional FEM or FDM. A series of numerical tests is conducted to assess the performance of the quadrature plate element in free vibration problems. Anisotropic and stepped thickness plates are investigated as well as mixed boundary conditions and point supports at the edges. In all cases, the results obtained are quite accurate.