He was born in Philadelphia, of a Quaker family, and was intended for a legal career, but gave up the law after a short time, and began writing full-time. His work was first published in the Columbia Magazine, and his first book, a treatise on the rights of women, was Alcuin: a Dialogue (1798). It shows the influence of William Godwin.
Having begun to write novels, Brown took on the editorship of The Monthly Magazine and American Review in 1799. Unusually, his novels were set in the USA. In 1803, however, he abandoned fiction and began a new magazine, The Literary Magazine and American Register. In 1804, he married, but he died of tuberculosis at the age of only thirty-nine.