In the era of big data, the collected data often contain outliers or present peak and thicktails and strong correlations between variables. To solve this problem, an efficient and robust variable selection method combining rank regression and Adaptive Elastic Net is proposed. The greatest advantage of this method is that it can not only effectively deal with the strong correlation among concomitant variables but also overcome the multicollinearity problem,and it can resist the influence of thicktailed distribution or outliers to achieve robust variable selection. In the aspect of numerical calculation, quadratic approximation and Newton iterative algorithm are used to obtain stable numerical solutions of the new variable selection method. Simulation results show that the proposed method performs better than the existing methods, especially for thicktailed distributions or outliers. Finally, through the tracking of CSI 100, an important stock market index in China, it is further demonstrated that this method has a good performance under effective samples.