Oxidative stress plays an important role in Alzheimer’s disease. To arrest oxidative stress, this contribution first identified and quantified phenolic bioactives present in the pulp and peel of pomegranate using high-performance liquid chromatography. Punicalagin β rendered the greatest antiradical activity as evaluated by on-line HPLC-ABTS method, which was followed by punicalagin α, gallic acid, and epicatechin. Furthermore, the scavenging activity against peroxyl and DPPH radicals, as well as the reducing power were investigated. Extracts obtained from the peel showed much higher phenolic contents and antioxidant properties than that of the pulp, hence being selected as potential inhibitor of acetylcholinesterase, a key enzyme involved in the progress of Alzheimer’s disease. Phenolics from pomegranate peel showed inhibition of acetylcholinesterase, which was dependent on the phenolic concentration. Therefore, pomegranate peel may be considered by the industry as a functional food ingredient and possibly for manufacturing of nutraceuticals.