The full waveform inversion method can be regarded as a large nonlinear minimization problem.In this method,Hessian operator exerts significant influence on the inversion result.Nevertheless,traditional optimization methods can only express the Hessian operator approximately,which will lead to low inversion accuracy,slow convergence speed,and the result that the parameter cannot be focused,especially for deep inversion region target with poor illumination.In contrast,the truncated Newton method,a new optimization method,can obtain the information of Hessian operator more accurately by the computation of the product of Hessian matrix and a known vector,and thus can solve the problem mentioned above.Therefore,this paper achieves full waveform inversion in the frequency domain based on truncated Newton method.And the model test shows that the truncated Newton method has more precise inversion results and improves the efficiency of inversion,especially for deep area with insufficient illumination compared with the limited memory BFGS (Limited-memory Broyden-Fletcher-Goldfarb-Shanno,L-BFGS) method.