Designing an effective criterion to select a subset of features is a challenging problem for hyperspectral image classification. In this paper, we develop a feature selection method to select a subset of class discriminant features for hyperspectral image classification. First, we propose a new class separability measure based on the surrogate kernel and Hilbert Schmidt independence criterion in the reproducing kernel Hilbert space. Second, we employ the proposed class separability measure as an objective function and we model the feature selection problem as a continuous optimization problem using LASSO optimization framework. The combination of the class separability measure and the LASSO model allows selecting the subset of features that increases the class separability information and also avoids a computationally intensive subset search strategy. Experiments conducted with three hyperspectral data sets and different experimental settings show that our proposed method increases the classification accuracy and outperforms the state-of-the-art methods.