Draper was a merchant's clerk in Boston, Massachusetts before coming to New York City where he settled as a merchant. He married a daughter of John Haggerty, and they had four children.
Draper was a friend of Daniel Webster and William H. Seward and a member of the Whig Party. He began his political career in the 1840s when he was appointed a member of the Board of Ten Governors, then in charge of New York City charities.
In the 1850s, Draper was Superintendent of Canal Repairs on the Cayuga and Seneca Canal.
He was one of the original Police Commissioners of the New York Metropolitan Police District, established on April 16, 1857, but resigned before the end of his one-year term.
He was Collector of the Port of New York from September 1864 to August 1865.
William B. Draper was his brother.
- The New York Civil List compiled by Franklin Benjamin Hough (page 439; Weed, Parsons and Co., 1858)
-  Obit in NYT on November 7, 1866
- Bio in The American Annual Cyclopædia and Register of Important Events published by D. Appleton and Company, 1867; page 275
|Party political offices|
|Chairman of the New York Republican State Committee
Henry R. Low
|Collector of the Port of New York