A graft copolymer of guar gum with acryl amide was made by using ammonium ceric nitrate/nitric acid as initiator. The effects of AM/GG, initiator concentration, reaction temperature and reaction time on polymerization were investigated. The results indicated that: The grafting ratio and comonomer conversion of grafting copolymerization were 147.05% and 87.7% when AM/GG=3:2, initiator concentration was 4mmol/L, reaction time was 4h and reaction temperature was 45℃. The largest molecular of graft copolymer could reach to 1.73x106. The analysis of IR spectrum and SEM turned out that AM did graft to the molecular chain of guar gum.TGA indicated that graft AM has no effect on the thermal stability of guar gum.