Fucoidans were degraded by hydrogen peroxide under the electron beam (2.5 MeV) with various radiation doses (5 kGy, 10 kGy, 15 kGy, and 20 kGy) at room temperature. The degradation property was analyzed with a gel permeation chromatography (GPC-MALLS) method. An average molecular weight of fucoidan decreased from 99,956 at the irradiation dose of 0 kGy to 6,725 at the irradiation dose of 20 kGy. The solution viscosity of fucoidans showed a similar pattern to the molecular weight change. The number of chain breaks per molecule (N) increased with increasing the irradiation dose and concentration of hydrogen peroxide. The radiation yield of scission value markedly increased with increasing the irradiation dose up to 15 kGy. Also a 10% hydrogen peroxide concentration was more efficient than that of 5%. The structures of degraded fucoidan samples were studied with Fourier transform infrared spectroscopy (FT-IR). The results showed that the degradation process did not significantly change the chemical structure or the content of sulfate group. The sulfur content of each sample was determined with an Elemental Analyzer. With increasing the concentration of hydrogen peroxide, the ratios of sulfur/carbon, hydrogen/carbon, and nitrogen/carbon slightly decreased. The antioxidant activities of fucoidans were investigated based on hydroxyl radical scavenging activities. The ability of fucoidan to inhibit the hydroxyl radical scavenging activity was depended on its molecular weight.