Abstract: Censored regression (``Tobit'') model is one of important regression models and has been widely used in econometrics. However, studies for variable selection problem in censored regression model are rare at the present references. In this paper, for censored regression model we propose a LASSO-type approach, diverse penalty L_1 constraint method (DPLC), to select variables and estimate the corresponding coefficients. Furthermore, we obtain the asymptotic properties of nonzero elements' estimation of regression coefficient. Finally, extensive simulation studies show that DPLC method almost possesses the same performance of selecting variables and estimation as generally best subset selection method (GBSS).