Seismic full-waveform inversion (FWI) can produce high resolution images of the Earth’s subsurface. Since full waveform modelling is significantly nonlinear with respect to velocities, Monte Carlo methods have been used to assess image uncertainties. However, because of the high computational cost of Monte Carlo sampling methods, uncertainty assessment remains intractable for larger data sets and 3D applications. In this study we propose a new method called variational full-waveform inversion (VFWI), which uses Stein variational gradient descent (SVGD) to solve FWI problems. We apply the method to a 2D synthetic example and demonstrate that the method produces accurate approximations to those obtained by Hamiltonian Monte Carlo (HMC). Since variational inference solves the problem using optimization, the method can be applied to larger datasets and 3D applications by using stochastic optimization and distributed optimization.