This study aimed to compare the anti-inflammatory effects of fucoidans from brown seaweeds (Saccharina japonica (SJ), Fucus vesiculosus (FV), Fucus distichus (FD), Fucus serratus (FS), and Ascophyllum nodosum (AN)), and determine the relationship between composition and biological activity. The anti-inflammatory activity was tested in vitro. It is believed that inflammation could be triggered by free radicals. Fucoidans from F. vesiculosus (FV1 and FV3) showed the strongest 1,1-diphenyl-2-picrylhydrazyl (DPPH) radical scavenging activity with an IC50 = 0.05 mg/mL. In the total antioxidant capacity (TAC) test, the activity was concentration-dependent. Notable, the TAC of fucoidans except samples of FV2 and SJ (which have a lower phenolic content) was higher than that of phloroglucinol. The TAC of fucoidans strongly and positively correlated with polyphenol content. A weak correlation was associated with xylose content. The synergistic effect for fucoidans was calculated for the first time using carbohydrates and polyphenols as model mixtures. The synergy in the DPPH test was found only for FV1 and FV3 (mixture effect ME = 2.68 and 2.04, respectively). The ME strongly positively correlated with polyphenols. The relationship of ME with fucose content was positive but moderate. It was first established that the anti-inflammatory effects of fucoidan could be mediated via the inhibition of protein denaturation. The inhibition was concentration-dependent and strongly correlated with the fucose content and moderate with sulfate content. The purified fucoidan FV2 showed the most promising activity (IC50 = 0.20 mg/mL vs. IC50 = 0.37 mg/mL for diclofenac sodium). Similar relations were also observed in the membrane protection model. Fucoidans were able to stabilize the cell membrane integrity of human red blood corpuscles (HRBC). The results of our study support the rationality of fucoidan use as a promising agent for the treatment of inflammatory-related diseases via mechanisms of radical scavenging, antioxidant activity, inhibition of protein denaturation, and HRBC membrane stabilization.