In this paper, we define a coboundary operator acting on the cochain in gauge potential space and establish a formula about Chern-Simons coboundary. The result can be employed to obtain the non-abelian anomaly, the gauge invariant Wess-Zumino effec-tive action and the Schwinger term etc. We show that the present approach covers Fad-deev's, Song's, and Zumino's approaches.