Since forward and backward diffusion cannot hold flow-like edges,and coherence enhancement diffusion cannot sharpen edges,a new edge-directed nonlinear diffusion equation to enhance image is put forward.The new model introduces forward and backward diffusion to the tensor diffusion,and gets a new diffusivity,which combines the merits of these two methods.The new model adapts an operator like coherence enhancement diffusion for edge orientation,and defines eigenvalues based on edge′s orientation such that the new tensor has positive diffusion coefficient in edge direction and negative diffusion coefficient in gradient direction.Both theory analysis and numerical results show that the new model has better enhancement result than coherence enhancing diffusion and forward and backward diffusion.