Norton was born in London to Thomas Norton, a merchant, and Elizabeth Merry Norton. He went to the University of Cambridge. In 1556, he studied law. He was a Member of Parliament. He was a Calvinist, and tortured Catholics. The English bishops grew to dislike him. He was charged with treason and sent to the Tower of London. He was soon released, but his health had grown poor. In March 1584, he died in his Bedfordshire home.
Norton began to write sonnets and other poems when he was 18. In 1560, he wrote the earliest English tragedy in blank verse, Gorboduc, with Thomas Sackville. He wrote many anti-Catholic pamphlets. He also translated John Calvin's Institutes (1561) and Alexander Nowell's Catechism (1570).