A finite element method with perfectly matched layers(PML) is developed for wave scattering from a two-dimensional cavity embedded in an infinite ground plane. Based on a variational formulation it uses the PML technique to truncate an unbounded computational domain to a bounded one. Hence, a PML problem instead of the original scattering problem is solved. Convergence of the PML problem to the scattering problem is analyzed. Numerical experiments illustrate competitive behavior of the proposed method.