Grafted copolymer (sodium alginate (Na. Alg)- acrylic acid (AcA)– methacrylic acid (MAcA)) was prepared by the gamma irradiation-induced copolymerization in the presence of N, N-methylene bisacrylamide (MBA) as a co monomer crosslinker. The functionality, morphology and thermal stability of the prepared copolymer have been examined using FTIR spectroscopy, SEM, and TGA-DTA, respectively. The surface morphology of the prepared grafted copolymer shows a smooth surface and relatively homogeneous appearance. Thermogravimetric analysis of the prepared grafted copolymer shows good thermal stability suitable for all the domain of practical application in which this polymer is used till near 400°C The effect of the preparation conditions on the swelling property of the prepared copolymer has been investigated and the mechanism of graft copolymerization through the irradiation process has been also discussed. The obtained results revealed that the optimum conditions for preparing a suitable grafted copolymer were by using 20% Acrylic acid, 10% Methacrylic acid and 0.4 wt % sodium alginate at irradiation dose 15 KGy with the addition of 0.03 % of MBA as a crosslinker.