He was born in the West Country, of a poor family. After being apprenticed to an Exeter bookseller he came to London and started up in business, advertising himself by a system of newspaper quarrels. His connexion with the anonymously-published Court Poems in 1716 led to the long quarrel with Alexander Pope, who took his revenge by immortalizing Curll in the Dunciad. Curll became notorious for his indecent publications, so much so that "Curlicism" was regarded as a synonym for literary indecency. In 1716 and again in 1721 he had to appear at the bar of the House of Lords for publishing matter concerning its members. In 1725 he was convicted of publishing obscene books, and fined in 1728 for publishing The Nun in her Smock and De Usu Flagrorum, while his Memories of John Ker of Kersland cost him an hour in the pillory.
When Curll in 1735 announced the forthcoming publication of "Mr Pope's Literary Correspondence," his stock, at Pope's instigation, was seized. It has since been proved that the publication was really instigated by Pope, who wanted an excuse to print his letters, as he actually did (1737-1741). In his forty years of business Curll published a great variety of books, of which a very large number, fortunately, were quite free from "Curlicisms." A list of his publications contains, indeed, 167 standard works.
For Curll's relations with Pope, see the Life of Pope, by Sir Leslie Stephen in the English Men of Letters series.