Spirulina platensis protein hydrolysates were prepared by digesting protein extracts with papain, and the hydrolysates were separated into 30, 10, and 3 kDa weights using membrane ultrafiltration. The 0–3 kDa low-molecular-weight Spirulina peptides (LMWSPs) proved the highest chemical antioxidant activity by 1,1-diphenyl-2-picrylhydrazyl (DPPH) radical scavenging ability, hydroxyl radical (·OH) scavenging activities and total antioxidant capacity. Cellular antioxidant ability of LMWPs fractions against 2000 μg/mL H2O2 induced oxidative damage of L02 cells were investigated. The MTT assay results displayed that LMWSPs at different concentrations (0–1000 μg/mL) had proliferation effect on the L02 cells and that treatment of the L02 cells with the 1000 μg/mL LMWSPs (0–3 kDa) significantly prevented H2O2-induced oxidative damage compared with control cells. Moreover, the 2′,7′-dichlorofluorescein diacetate (DCFH-DA) fluorescent probe assay showed that the levels of ROS and NO were significantly lower in the experimental group that was treated with the peptides for 24 h than in the control group. Furthermore, using the corresponding kits, the treatment inhibited the reduction of SOD activity and the increase of MDA contents in the L02 cells. Therefore, LMWSPs (0–3 kDa) may have potential applications in antioxidant and liver health products.