Generalized coarse-mesh finite difference(GCMFD) method,which uses generalized-geometry coarse meshes to speed up the method of characteristics(MOC),is proposed.A method adjusting width factor automatically is adopted in the GCMFD method.The GCMFD method is adopted in a 3-D neutron transport MOC code TCM.Numerical tests are used to verify acceleration effect of GCMFD in TCM.It shows that the GCMFD method can use generalized-geometry coarse meshes to accelerate MOC iteration,and the GCMFD method with automatically adjusting width factor has good acceleration effect.