A novel silver nanoparticle-based (AgNP) method and two modified procedures, ferric reducing antioxidant power (FRAP) and 2,2′-diphenyl-1-picrylhydrazyl (DPPH), were used for determination of antioxidant capacities of the ethanolic, methanolic, methanolic–aqueous (1 : 1 v/v) and aqueous extracts of rapeseed and its products. The AgNP method based on the electron-transfer reaction between silver ions and antioxidants in an optimized ammonium buffer medium (pH = 8.4) and determination of silver nanoparticle formation has been elaborated. The novel AgNP method was validated using sinapic acid, gallic acid, caffeic acid, ascorbic acid and quercetin as standard antioxidant solutions in concentration ranges of 0.03–0.21 µmol mL⁻¹, 0.02–0.20 µmol mL⁻¹, 0.01–0.18 µmol mL⁻¹, 0.03–0.30 µmol mL⁻¹ and 0.001–0.009 µmol mL⁻¹. The calculated detection (DL = 0.01, 0.02, 0.009, 0.02 and 0.0004 µmol mL⁻¹ for sinapic, gallic, caffeic, ascorbic acids and quercetin, respectively) and quantification limits (QL = 0.04, 0.06, 0.03, 0.08 and 0.001 µmol mL⁻¹ for sinapic, gallic, caffeic, ascorbic acids and quercetin, respectively) confirm linearity concentration ranges for determination of antioxidant capacity by AgNP assay. The average antioxidant capacities of the studied rapeseed samples ranged between 14.7 and 126.2 µmol sinapic acid per gram for the proposed AgNP method, 7.4–112.7 µmol sinapic acid per gram for the FRAP method and 39.1–339.8 µmol sinapic acid per gram for DPPH assay. The methanol–water mixture (1 : 1 v/v) was the most efficient solvent for extraction of antioxidants from the studied rapeseed samples. There are significant, positive correlations between the novel AgNP and the modified FRAP, DPPH and FC methods for all extracts of the studied rapeseed samples (r = 0.7564–0.8516, p < 0.001). Satisfactory values of precision (RSD = 1.2–4.4%) and accuracy (recovery = 95.6–104.6%, except methanolic extracts) demonstrate the benefit of the proposed AgNP method for analysis of the antioxidant capacity of rapeseed samples. Results of the principal component analysis (PCA) indicate that there are differences between the total amounts of antioxidants in rapeseed samples extracted by different solvents.