Hydrogels based on sodium alginate (SA) and partially neutralised poly(acrylic acid) were obtained by radical polymerisation. The hydrogels were cross-linked with N,N'-methylenebisacrylamide (MBA), simultaneously grafting the resulting polymer onto SA. The findings of the FTIR spectroscopy showed that all of the hydrogels were effectively synthesized and sodium alginate was chemically bonded with the poly(sodium acrylate) matrix. DSC analysis of the melting heat and glass transition parameters indicated that the hydrogel structure had changed as a result of the cross-linking process. Sodium alginate and MBA were tested at different concentrations to determine how they affected the hydrogel properties. A very high content of the biopolymer, i.e., sodium alginate, was used in our research, up to 33 wt%. This resulted in durable and stable hydrogels with a very high ability to uptake water, comparable to hydrogels based on synthetic polymers only. The ability to swell is inversely proportional to the quantity of MBA present. By increasing the amount of sodium alginate in the hydrogel, the ability of the hydrogel to absorb water is reduced. However, water uptake remains relatively high at 350 g·g, even for the hydrogel with the highest SA content.