Abstract: This paper establish a first passage time model based on the Merton's structural model by using the method of geometric Brownian motion. In this paper, we consider the accounting noise and historical default record and then introduce a new incomplete information hypothesis. Besides, we introduce the stock's liquidity value into the model, and apply its method measurement which based on Merton's structural model to the first passage time model to obtain the endogenous default boundary. Based on the incomplete information, the conditional default probability is derived by using the default boundary. And at the last of this passage, we analysis the effect of the correlation between stock's price and company assets on the default probability.