Abstract: This paper analyzed the factors affecting the gradient accuracy from the view of back propagation operator, and proposed a new method for gradient construction of full waveform inversion based on complex frequency attenuation back propagation operator. The gradient construction noise can be suppressed with the proposed method. During the inversion, the BFGS (L-BFGS) method is adopted to balance the relation between the huge storage capacity and the accuracy. The tests based on single layer model, overthrust fault model and sag model validate that the proposed method can suppress the noise in the gradient construction comparing with the conventional gradient method. Then the full waveform inversion is tested on a complex faulted blocks model, and the inversion accuracy is compared with that of the conventional method, proving that the proposed method in this paper is correct and effective in improving the gradient accuracy.