Full-waveform inversion (FWI) is a powerful tool for imaging underground structures with high resolution; however, this approach commonly suffers from the cycle-skipping issue. Recently, various FWI methods have been suggested to address this problem. Such methods are mainly classified into either data-space manipulation or model-space extension. We developed an alternative FWI method that belongs to the latter class. First, we define the virtual scattering source based on perturbation theory. The virtual scattering source is estimated by minimizing the differences between observed and simulated data with a regularization term penalizing the weighted virtual scattering source. The inverse problem for obtaining the virtual scattering source can be solved by the linear conjugate gradient method. The inverted virtual scattering source is used to update the wavefields; thus, it helps FWI to better approximate the nonlinearity of the inverse scattering problem. As the second step, the virtual scattering source is minimized to invert the velocity model. By assuming that the variation of the reconstructed wavefield is negligible, we can apply an approximated full Newton method to the velocity inversion with reasonable cost comparable to the Gauss-Newton method. From the numerical examples using synthetic data, we confirm that the proposed method performs better and more robust than the simple gradient-based FWI method. In addition, we show that our objective function has fewer local minima, which helps to mitigate the cycle-skipping problem.