Peter Neilson may refer to:
Peter Neilson (footballer) (1890 – after 1913), Scottish footballer Peter Neilson (poet) (1795–1861), Scottish businessman, author, and naval inventor Peter Neilson (politician born 1879) (1879–1948), New Zealand MP for Dunedin Central Peter Neilson (politician born 1954) (1954–2022), New Zealand MP for Miramar
See also Peter Nielsen (disambiguation), multiple people