The use of isopropanol as a hydroxyl radical scavenger on the radiosynthesis of alginate-stabilized silver nanoparticles (AgNPs) can limit its application in nanomedicine. Meanwhile, optimum condition for gamma irradiation synthesis of alginate-stabilized AgNPs without addition of a hydroxyl radical scavenger has not been reported yet. In this study, the optimization of this process was carried out using response surface methodology (RSM) combined with Central Composite Design (CCD). The three processing conditions, i.e. radiation dose, precursor silver ion concentration, and alginate concentration were selected as decision variables to maximize two responses in terms of the conversion yield and AgNP concentration responses. The results indicated that the regression model of conversion yield and AgNP concentration fit linearly with the two-factor interaction and the linear model, respectively. The significant effect of the alginate factor on the conversion yield indicates the dual stabilizing-scavenging role of the alginate. The optimum conditions derived from CCD-RSM were obtained at a 20 kGy radiation dose, 7.78 mM precursor silver ion concentration, and 1.2 % (w/v) alginate concentration with the desirability of 0.731. The actual experimental results were 65.43% conversion yield and 480.91 ppm AgNP concentration, which were within the prediction interval at confidence of 95 %. The AgNPs under the optimum condition had a spherical shape, 97.4 % volume of size distribution at 6.50-28.21 nm, and zeta potential of -28.3 mV.