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A variational model which is used to locate at the boundary of the object in the designated region is presented in this paper. This is done by adding an intersect area term into our model, which will play an important role in this paper. In this model, we need to construct an energy functional ε using two level set functions. One is used to capture the object of interest, the other one indicates image region which should be corrected. By minimizing the proposed model with respected to both two functions,the approach permits to segment the more accurate boundary. We implement our model with two algorithms, advantages and disadvantages of the two algorithms are discussed according to the experiment result. At the same time, we compare our model with a model proposed by Chunming Li et al. The result shows that our model is more accurate.