Curtis was born in the Memorial Hospital, Old Trafford, Manchester, in 1956. He grew up in the Hurdsfield area of Macclesfield and from a young age he exhibited talent as a poet. Although awarded a scholarship to attend the The King's School, Macclesfield, at the age of 11, Curtis never pursued academic success. As he grew older, his ambitions and hopes became focused on a pursuit of art and literature and, ultimately, music. Curtis was employed as a civil servant in Manchester and later in Macclesfield.

He was influenced by the writers William Burroughs, J. G. Ballard and Joseph Conrad (the song titles "Interzone", "Atrocity Exhibition",[1] and "Colony" coming from the three authors, respectively), and by the musicians David Bowie, Iggy Pop and Jim Morrison, lead singer with one of his favourite bands, The Doors.

Curtis married his high school girlfriend Deborah Woodruff on 23 August 1975, when he was 19 and she was 18. They remained married until his death; his widow is still alive. They had one child, Natalie, who was born on 16 April 1979.