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In this paper, the interior point based continuous method is proposed for linear programming. The continuous method model can be viewed as the continuous realization of the existing interior point method for linear programming. Our study will be under the framework of the continuous method for optimization. As a result, we are able to study the behaviors of these continuous method models in a unified format. A key component of the continuous method is an ordinary differential equation (ODE), which is established based on the interior point method for linear programming. The properties of the ODE along with the convergence issues will be addressed.