We developed a travel-time tomography method to reveal general anisotropic media using the shortest path method. Introducing the local coordinate system fixed to the symmetric axis of an anisotropic medium, the rotation angles of the local coordinate system and elastic parameters in the local coordinate system are unknown parameters to be solved. The method is basically applicable to general anisotropic media. Using synthetic travel-time data, we applied our method to a hexagonal symmetric anisotropic medium and orthorhombic symmetric anisotropic medium to examine the method. The targeted symmetric anisotropic media were successfully restored, although the range of the rotation angle is limited.