Endogenous variables are often encountered when discussing the relationship between covariates and response variables. Most of the existing researches on endogenous variables are discussed in the framework of least squares objective function. However,this method is not robust. In this paper, the exponential squared loss estimation method is used to construct the robust estimation of regression coefficient in the model. In order to overcome the bias of endogenous variables on the estimation, instrumental variables are used to eliminate the endogeneity of covariates, and then the exponential squared loss estimation of regression coefficients is constructed. For the exponential squared loss objective function, the estimation process of selecting effective adjustment parameters is proposed. Under some regular conditions, the asymptotic normality of the proposed estimator is studied. In the simulation study, six estimation methods are compared, including the naive least squares estimation, the naive M estimation, the naive exponential squared loss estimation, the least squares estimation using instrumental variables, the M estimation using instrumental variables, and the exponential squared loss estimation using instrumental variables. The simulation results show that the proposed method can effectively eliminate the endogeneity of covariates, and has good robustness. Finally, the wage and schooling data collected from the survey of identical twins is analyzed by our proposed method.