In this paper, we mainly consider the estimation of the Tobit model when the covariates are measured with the errors. It is unnecessary to assume the structure of the measurement error model or the known error variance for the proposed method. At the same time, the repeated measurements data are not required. With the help of the auxiliary variable, an estimator of the true variable can be obtained by applying the local smoothing method. The true variables are replaced by their estimators and then an estimator of the regression coefficient can be defined via minimizing the corrected least squares objective function. An algorithm is presented to compute the proposed estimator and the asymptotic normality of the proposed estimator is acquired. The numerical simulation studies are conducted, which show that the proposed method performs better than the naive method. The proposed method is employed to analyze a revised real data of Duchenne Muscular Dystrophy.