Elaeagnus glabra f. oxyphylla (Elaeagnaceae) is a small evergreen tree with narrow lanceolate leaves that is native to Korea. In this work, we studied the chemical composition of E. glabra f. oxyphylla branches (EGFOB) for the first time. Additionally, we evaluated the effects of the ethanol extract of EGFOB and each of its chemical components on key mediators of Alzheimer’s disease (AD), namely, amyloid-β (Aβ) aggregation and oxidative stress. The ethanol extract of EGFOB decreased Aβ aggregation (IC50 = 32.01 µg/mL) and the levels of the oxidative free radicals 2,2′-azino-bis(3-ethylbenzothiazoline-6-sulphonic acid) (ABTS) and 2,2-diphenyl-1-picrylhydrazyl (DPPH) (IC50 = 11.35 and 12.32 µg/mL, respectively). Sixteen compounds were isolated from EGFOB. Among them, procyanidin B3 (8), procyanidin B4 (9), and helichrysoside (13) significantly inhibited Aβ aggregation (IC50 = 14.59, 32.64, and 44.45 μM, respectively), indicating their potential as bioactive compounds to control Aβ aggregation. Furthermore, these compounds markedly enhanced in vitro scavenging activity against ABTS (IC50 = 3.21–4.61 µM). In the DPPH test, they showed lower scavenging activity than in the ABTS test (IC50 ≥ 54.88 µM). Thus, these results suggest that EGFOB and specifically compounds 8, 9, and 13 may be beneficial in AD prevention and treatment through their antioxidant and anti-Aβ aggregation activities.