Abstract: A fast marching algorithm is proposed to solve shape-from-shading problems and the general Eikonal equations.First,the expansion of isolines is recorded and tracked.Then,the values of nodes in expanding band are updated by upwind scheme once or twice in different orders. The time complexity is proven to be O(N).Experimental results show that the algorithm can improve the numerical efficiency and accuracy of existing fast marching methods,solve adequately mult-i source and shape-from-shading problems,and is much faster than the fast sweeping method in complicated situations.