In this talk, we study a corporate bond-pricing model with credit rating migration and a stochastic interest rate. The volatility of bond price in the model strongly depends on potential credit rating migration and stochastic change of the interest rate. This new model improves the previous existing models in which the interest rate is considered to be a constant. The existence, uniqueness and regularity of the solution for the model are established. Moreover, some properties including the smoothness of the free boundary are obtained. Furthermore, some numerical computations are presented to illustrate the theoretical results. This talk is based on a joint work with Xinfu Chen at University of Pittsburgh and Professor Jin Liang and Dr. Yuan Wu at Tongji University.