In many engineering applications, it is necessary to calculate the min-area encasing box of a circumscription. In this paper, an algorithm for generating the min-area rectangle encasing box, based on revolving angle, is investigated and hence put forward. The algorithm computes the areas of the outer rectangular bounds of a closed contour in different revolving angles θ by dispersing approach where 0＜θ＜π/2 because of the axial symmetry. It is very simple, straight forward and highly efficient. The complexity of its computing time reaches O(n·k). Practical applications suggest its usefulness and efficiency.