Fucoidan is a multifunctional marine carbohydrate polymer that differs in its chemical composition and bioactivity both between seaweed species and within species from different locations across the globe. In this study, fucoidan was extracted from the sporophyll of Undaria pinnatifida grown in Weihai, Shandong Province, China. Fucoidan fractions with molecular weight cutoffs (MWCO) of >300 kDa and <10 kDa were obtained via dialysis. The fucoidan standard from Sigma (Fstd, ≥95, CAS: 9072-19-9), fucoidan crude extract (WH), >300 kDa fraction (300k) and <10 kDa fraction (10k) were compared in terms of chemical composition and antioxidant capacity. Based on Fourier transform infrared spectroscopy (FT-IR) analysis, Fstd, WH, and 300k all showed strong bands around 830 cm−1, corresponding to the sulfate substituent in the molecule. The results showed that compared with WH and 300 k, the degree of sulfation at 10k was the lowest. From Nuclear magnetic resonance spectroscopy (NMR) result, the four fucoidan samples all contain α-L-fucose. The primary antioxidant ability of the 10k is significantly higher than that of the 300k, WH, and Fstd, but the secondary antioxidant capabilities of the 10k and 300k were similar, and both were higher than that of the butylated hydroxyanisole (BHA). The ferric reducing antioxidant ability was higher in the 300k and WH fractions. This demonstrates that fucoidan extracted from U. pinnatifida grown in Weihai, China should be a useful nutraceutical resource.