Abstract: The accurate calculation of anisotropic first arrival traveltime and raypath is critical for migration imaging and tomographic inversion.The shortest-path method based on graph theory can get the traveltime as well as the raypath with high stability.Thus,we proposed a new shortest-path ray tracing algorithm for anisotropic medium.To compute the traveltime in a grid,Newton downhill method is used to solve the equation relating group angle with phase angle.By this way,a more accurate phase angle can be achieved from a group angle,and then a more accurate group velocity and traveltime can be obtained.Correspondingly,the shortest-path method can be applied to strong anisotropic medium.Finally,this ray tracing algorithm was applied to homogeneous anisotropic medium,a layered model and a complex model,and its effectiveness was proved through comparing the computed traveltimes with those using the finite difference implementation of elastic wave equation.