Abstract: In general, we apply finite element method with triangular meshes to accurately modeling wave field under complex structures; however, in the condition of the same number of nodes, computational accuracy of triangular element is lower than that of rectangular element. It is difficult to implement the computer program which locates the non-zero elements of global stiffness matrix when we adopt triangular elements to fit complex geometrical interface. Using rectangular elements to divide geological model containing dipping or rugged interface will result in diffraction noise, and infilling grid will increase computational amount. For these reasons, this paper applies finite element method to solve 2-D acoustic wave equation, arbitrary quadrilateral meshes is adopted to fit dipping or rugged interface, which can avoid introducing “ladder” interface resulted from discrete rectangular grid, and discrete diffraction noise is eliminated effectively in the condition of no increasing computational amount and memory occupation. Diagonal lumped mass matrix is used to replace consistent massmatrix to avoid matrix inversion and improve the computational efficiency of explicit finite element method. In addition, we employ compact storage format to store global stiffness matrix, and the elements need to be stored in each row is no more than 5, the zero elements are not involved in computing at the same time, by this method, not only reducing the memory occupation, but also improving the computational efficiency.