Hen’s egg white lysozyme (HEWL) is one of the major egg white proteins with well demonstrated antimicrobial activity. Bioactive peptides other than antimicrobial peptides from HEWL have not been reported; therefore, the purpose of the study was to explore new bioactivities of lysozyme-derived bioactive peptides. HEWL was hydrolysed with Alcalase and fractionated by cation-exchange chromatography. The Alcalase HEWL hydrolysate and its fractions were analyzed for inhibitory activities against calmodulin-dependent phosphodiesterase (CaMPDE) and antioxidant activities using oxygen radical absorbance capacity-fluorescein (ORAC-FL), 2,2′-Azino-bis(3-ethylbenzothiazoline-6-sulfonic acid) diammonium salt radical cation (ABTS+) and 2,2-di(4-tert-octylphenyl)-1-picrylhydrazyl (DPPH) radical scavenging methods. The fractionated peptides had higher CaMPDE inhibition activity, ORAC-FL value and ABTS+ scavenging activity than those of the hydrolysate. Peptide sequences in the most overall active fractions were characterized by LC–MS/MS. Our results showed that HEWL hydrolysate and its peptide fractions may serve as useful ingredients in the formulation of functional foods and nutraceuticals.