This　article　proposes　a　novel　iterative　weighted　group　thresholding　method　for　group　sparse　recovery　of　signals　from　underdetermined　linear　systems.　Based　on　an　equivalent　weighted　group　minimization　problem　with　l(p)(p)-norm　(0　＜　p　＜=　1),　we　derive　closed-form　solutions　for　a　subproblem　with　respect　to　some　specific　values　of　p　when　using　the　proximal　gradient　method.　Then,　we　design　the　corresponding　algorithmic　framework,　including　stopping　criterion　and　the　method　of　nonmonotone　line　search,　and　prove　that　the　solution　sequence　generated　by　the　proposed　algorithm　converges　under　some　mild　conditions.　Moreover,　based　on　the　proposed　algorithm,　we　develop　a　homotopy　algorithm　with　an　adaptively　updated　group　threshold.　Extensive　computational　experiments　on　the　simulated　and　real　data　show　that　our　approach　is　competitive　with　state-of-the-art　methods　in　terms　of　exact　group　selection,　estimation　accuracy,　and　computation　time.