The rapid convergence rate, high fidelity learning outcome and low computational cost are key targets in solving the learning problem of the complex physical system. Guided
by physical laws of wave propagation, in full waveform inversion (FWI), we learn the subsurface images through optimizing the media velocity model in a large scale non-linear problem. In this paper, we combine randomized subsampling techniques with a second-order optimization algorithm to propose the Sub-Sampled Newton (SSN) method for learning velocity model of FWI. By incorporating the curvature information, SSN preserves comparable convergence rate to Newtons method and significantly reduces the iteration cost by approximating the Hessian matrix through a non-uniform subsampling scheme. The numerical experiments demonstrate that the proposed SSN method has a faster convergence rate, and achieves a more accurate velocity model in terms of mean squared error than commonly used methods.