To solve the problem of interest rate risk management with default risk, we point out the necessity of studying the problem of interest rate risk management for bonds with default risk within the framework of the asset and liability management for commercial banks, obtain the formula of Duration of bond with default risk and establish a goal programming model for the interest rate risk, mean-absolute deviation constraint, other related balance constraints and the goal constraint. After giving a numerical example, we discuss the impact of the existence of default risk on the interest rate risk management of banks