Curtis was born on November 4, 1809 in Watertown, Massachusetts. He graduated Harvard University in 1829 and went on to Harvard Law School. He first established a law practice in Northfield in 1831, but moved to Boston in 1834 where he joined a law firm. In 1849 he was elected to the Massachusetts State Legislature. In 1851 as the head of the committee on judicial reform Benjamin presented to the legislature the Practice Act of 1851. President Millard Fillmore nominated Curtis to the Supreme Court in 1851.
In 1857 Curtis resigned from the court and returned to private practice. He died in 1874.