Peter Neilson (1879–1948) was a New Zealand politician of the Labour Party.
He represented the electorate of Dunedin Central in Parliament from 1935 to 1946, when he retired. He had unsuccessfully stood for the seat in 1931.
He was born in Dunedin, a baker, and was a business partner of J. W. Munro, also a Labour MP, from 1914. He had been active in the Socialist Party and Social Democratic Party, and had been on the Dunedin City Council and Maori Hill Borough Council.