A local discontinuous Galerkin (LDG) method is developed for solving the Camassa-Holm (CH) equation which contains nonlinear high-order derivatives. The CH equation is split into a series of linear ordinary differential equations on which the LDG method is developed. The stability of the LDG method is established followed by the error estimates. Examples from the smooth traveling waves, peaked traveling waves and their interactions and the Plateau traveling waves are considered to illustrate the accuracy of the method. The LDG methods are flexible for general geometry, unstructured meshes and have parallel efficiency.