I have presented a new method, named local ray-tracing method, for propagating wavefronts. Through the wavefront propagation process, the traveltimes and geometrical amplitudes of seismic waves are computed on an even grid, which is similar to a finite difference method for traveltime calculation. Because the method assumes a continuous velocity representation and propagates local circular wavefronts by following local rays, it gives more accurate traveltimes and amplitudes than a finite-difference method. The method can also compute the traveltimes of multiple arrivals. The traveltimes and amplitudes calculated by this method can be used in the Kirchhoff depth migration.