Edge detection is the first step and very important step in image analysis. We cast edge detection as a problem in cost minimization. This is achieved by the formulation of a cost function that evaluates the quality of edge configurations. The cost function can be used as a basis for comparing the performances of different detectors. This cost function is made of desirable characteristics of edges such as thickness, continuity, length, region dissimilarity. And we use a simulated annealing algorithm for minimum of cost function. Simulated annealing are a class of adaptive search techniques that have been intensively studied in recent years. We present five strategies for generating candidate states. Experimental results(building image and test image) which verify the usefulness of our simulated annealing approach to edge detection are better than other operator.