The first-to-default Credit Default Swap (CDS) with multiple assets is priced when the default barrier is changing over time, which is contrast to the assumption in most of the structural-form models. The survival function of each asset follows the lognormal distribution and the interest rate is constant over time in this article. We define the joint survival function of these assets by employing the normal and Student-t copula functions to characterize the dependence among different default probability of each asset. In addition, we investigate the empirical evidences in the pricing of CDS with two or three companies by changing the values of parameters in the model. The more interesting results show that the joint default probability increases as these assets are more positive correlated. Consequently, the price of the first-to-default CDS is much higher.