Variable selection in finite mixture of regression (FMR) models is frequently used in statistical modeling. The existing studies on FMR models mainly base on the normality ass-umption of regression error. However, this assumption is not suitable for studying asymmetric data. The performance of the mode is better than that of the mean for skewed data. This paper proposes a variable selection method for mixture of mode regression models basing on the skew-normal distribution. The consistency and the Oracle property are proved. A modified EM algorithm is developed to estimate the parameters in the model. Simulation studies are conducted to investigate the performance of the proposed methodologies. A real example is further provided to investigate the performance of the proposed methodologies.