In this study, we developed a novel offline high-performance liquid chromatography (HPLC) method based on 2,2′-azobis(2-amidinopropane) dihydrochloride (AAPH) radicals for antioxidant screening in 20 polyphenolic compounds and used the Trolox equivalent antioxidant capacity assay to evaluate their antioxidant activity. Compared to the existing offline HPLC methods based on 2,2′-azino-bis(3-ethylbenzothiazoline-6-sulfonic acid (ABTS) and 2,2-diphenyl-1-picrylhydrazyl (DPPH), the offline HPLC method based on the AAPH radical is more sensitive. Additionally, we applied this method to Lepechinia meyenii (Walp.) Epling extract and screened out seven antioxidants, caffeic acid, hesperidin, rosmarinic acid, diosmin, methyl rosmarinate, diosmetin, and n-butyl rosmarinate, which are known antioxidants. Therefore, this study provides new insights into the screening of antioxidants in natural extracts.