This paper studies a class of non-autonomous competition and cooperation model of enterprises with two time delays. Sufficient conditions for the ultimately boundedness and global attractivity of the model are derived by using inequality techniques and the construction of multiple Lyapunov functions. As an application of the main results, also studied are three special cases of the considered model, and obtained the sufficient conditions on the ultimately boundedness and global attractivity of the considered models. Finally, two numerical examples further verified the validity and effectiveness of the obtained results. From the main results and two numerical examples, it can be concluded that the two discrete delays affect the global attractiveness of the model. The obtained results improvemed and extended the previously related studies.