Let C be a set of colors, and let  be an integer cost assigned to a color c in C. An edge-coloring of a graph  is assigning a color in C to each edge  so that any two edges having end-vertex in common have different colors. The cost  of an edge-coloring f of G is the sum of costs  of colors  assigned to all edges e in G. An edge-coloring f of G is optimal if  is minimum among all edge-colorings of G. A cactus is a connected graph in which every block is either an edge or a cycle. In this paper, we give an algorithm to find an optimal edge-   coloring of a cactus in polynomial time. In our best knowledge, this is the first polynomial-time algorithm to find an optimal edge-coloring of a cactus.