In this work, the modal damping of multilayered, fiber-reinforced polymer composite laminates with an arbitrary geometry have been computed using a mixed finite element-meshless method. The meshless node distribution scheme is used in conjunction with the Lagrangian quadrilateral interpolating functions to ensure the continuity of interelemental displacements. Furthermore, since the distribution of the elements is not confined to the geometry of the problem, any arbitrary geometry can be readily analyzed by using the same node and element distributions. Using the classical plate theory, together with a structural damping model, modal response results have been produced for a number of multilayer fiber-reinforced polymer plate geometries, including triangular and circular as well as rectangular plates with different combinations of free and clamped edges. Comparison of these results with those reported in the literature shows that the proposed method can predict the modal properties of fiber-reinforced polymer laminates with arbitrary geometries and boundary conditions with a good degree of accuracy.