Characteristic function  has been applied widely in practice. Many important practical problems, such as single chance constrained optimization problem, can be formulated as the problems associated with the characteristic function, the problem usually is non-convex and non-smooth. In this paper, we propose a smoothing D.C. function  based on Chen-Harker-Kanzow-Smale smooth plus function. Some properties of function  are discussed. Under certain conditions, proposed smoothing D.C. function is convergent to  when the parameter involved is small enough.

characteristic function, Chen-Harker-Kanzow-Smale smooth plus function, D.C. approximation.