In this paper, we studied the scattered layout problem in a circular zone by establishing a non-linear mathematical programming model, which can be solved by gradient method after transformed into the maximum value search for a no-constrained optimization problem when the number of layout points is less. However, the gradient method will become extremely inefficient or even can not work if the layout points are many. In order to solve this problem we proposed an approximation algorithm with the bound of 1/2 for fast solution, And several cases are given to verify the rationality and performance of the approximate algorithm at last. In a sense, the conclusions and approximation algorithm of this article enrich and improve the theories of the scattered layout problem.