Neonatal male circumcision (NMC) is being scaled up in Zambia and elsewhere in Southern Africa as a long-term HIV prevention strategy. We conducted 12 focus group discussions with 129 parents and grandparents in Lusaka, recruited from two sites providing free NMC services and information about NMC, to explore the acceptability of circumcising newborn boys. Most participants recognized the benefits of circumcision for HIV prevention, and the advantages of circumcising their children and grandchildren at a young age. Fear of negative outcomes, concerns about pain, and issues around cultural identity may challenge NMC uptake. To effectively promote the service, the upper age limit for NMC must be emphasized, and fathers must be targeted by messaging campaigns.