Since　Magnetic　resonance(MR)　Images　commonly　possess　a　blocky　structure　and　have　sparse　representations　under　certain　wavelet　bases,　total　variation　(TV)　and　wavelet　domain　1　norm　regularization　are　often　enforced　together　(TV-wavelet　method)　to　improve　the　recovery　accuracy.　However,　this　model　ignores　that　a　family　of　wavelet　coefficients　has　a　natural　grouping　of　its　components.　In　this　paper,　we　propose　a　new　TV-Group　sparse　model　which　combines　TV　and　wavelet　domain　group　sparse　penalty.　The　corresponding　algorithm　based　on　composite　splitting　method　is　employed　to　approach　this　TV-Group　sparse　model.　Experimental　results　show　that　our　model　can　obviously　improve　both　objective　and　subjective　qualities　of　MR　image　recovery　comparing　with　the　TV-wavelet　model.　©　2013　IEEE.