The computational tasks involved in the nonlinear tomographic traveltime inversion can be efficiently accomplished by using finite difference methods. The traveltimes can be computed by solving the eikonal equation. The derivatives of traveltimes with respect to the parameters of a slowness model can also be computed by solving a first-order linear partial differential equation. This new approach greatly reduces the computational cost imposed by the conventional ray tracing method. It ensures the proper treatment of the first-arrival traveltimes. Furthermore, the method handles the slowness model expanded with arbitrary basis functions, which is useful in incorporating geological structure interpretation into the inversion process. I expect that the new method will improve the result of the inversion.