Abstract: A method is presented to extend the Convolution Perfectly Matched Layer (CPML),which bases on the complex coordinates transformation and complex frequency shifted stretched-coordinate metrics,to the 2D acoustic equation calculated with the method of Finite Element Method (FEM).This non-physical layer is used at the computational edge of a FEM as an Absorbing Boundary Condition (ABC) to truncate unbounded media.In this paper,the CPML equations have been presented in frequency domain and in time domain,respectively,and the calculations have been realized in the FEM software of COMSOL.The main advantage of CPML over the classical PML layer is that it is based on the unsplit components of the wave field leading to a more stable,highly effective absorption and a more facility to realize.The results of numerical simulation demonstrate that CPML has better absorbability than PML and it absorbs the outgoing energy more effectively.