In this paper, we construct the forward rate model with both the default risk and the jump risk to clarify the effect of the default risk through the implied volatility. For tractability, the Vasicek-type hazard rate model is applied to the default risk instead of the traditional point process. As well known that the model with jump risk can express the smile or the skew, this paper is shows that the implied volatility including the hazard rate can also illustrate smile or skew through a numerical example. Furthermore, it is clarified that there are differences of influence caused by default risk according to the exercise price and the time interval.