In　this　paper,　we　investigate　the　sparse　group　feature　selection　problem,　in　which　covariates　posses　a　grouping　structure　sparsity　at　the　level　of　both　features　and　groups　simultaneously.　We　reformulate　the　feature　sparsity　constraint　as　an　equivalent　weighted　l1-norm　constraint　in　the　sparse　group　optimization　problem.　To　solve　the　reformulated　problem,　we　first　propose　a　weighted　thresholding　method　based　on　a　dynamic　programming　algorithm.　Then　we　improve　the　method　to　a　weighted　thresholding　homotopy　algorithm　using　homotopy　technique.　We　prove　that　the　algorithm　converges　to　an　L-stationary　point　of　the　original　problem.　Computational　experiments　on　synthetic　data　show　that　the　proposed　algorithm　is　competitive　with　some　state-of-the-art　algorithms.　©　2013　IEEE.