Custis was born probably early in the 1740s on the Northampton County estate of his parents, Edmund Custis and Katherine Sparrow Custis. Still a minor at the time of his father’s death in 1748, Custis inherited four slaves and a 300-acre plantation. By the mid-1760s he had vacated his pew in the local church, sold his Northampton County property, and moved to neighboring Accomack County. Custis’s activities during the next decade remain uncertain, but by 1779 he had begun to acquire land in Accomack, including property near Onancock, which became his home base. On an unrecorded date between December 1, 1779, and February 29, 1780, Custis married Elizabeth Drummond. It is not known whether they had any children. During the next decade he and his wife bought and sold a number of properties in the county, including town lots in Onancock.
Although Custis appears to have supported the patriot cause during the Revolutionary War, he often exhibited strong pro-British sentiments, as did a significant minority on the Eastern Shore. In 1781 he joined several other men in requesting that the governor reduce or remit the sentence of a local minister convicted of aiding the enemy. The next year the governor and theinitiated an investigation into Custis’s wartime dealings with British merchants, but prominent local politicians came to his defense and the issue was eventually dropped. Custis continued to advance in local politics, and in April 1785 he became a vestryman of Saint George’s Parish. On April 1, 1787, he outpolled three other candidates to win one of two seats representing the county in the House of Delegates. He was not appointed to any standing committees. While in the General Assembly he supported legislation authorizing payment of debts to British subjects and their American partners and insisted that glebe lands remain in the hands of the new Episcopal Church.
On March 25, 1788, Custis was elected one of two Accomack County delegates to the convention called to consider the proposed constitution of the United States. Despite a dire warning from “An American” published in several newspapers in May and June that the Eastern Shore would be set adrift if Virginia did not ratify the, Custis joined other antifederalists in voting to require prior amendments to the Constitution and after that effort failed voted against ratification on June 25. Two days later he voted to restrict the federal taxing power. His fellow delegate from Accomack, George Parker, voted exactly the opposite on the three key issues.
Reelected to the House of Delegates in 1788 and 1789, Custis served on the Committees of Claims and of Propositions and Grievances during both terms. He generally voted with the majority on key legislation. In December 1788 Custis mounted an unsuccessful attempt to gain a seat on the Council of State. He placed last among three candidates and lost his reelection bid to the House of Delegates on April 27, 1790.
Custis acquired more than 1,000 acres in Accomack County and owned more than a dozen slaves during the 1780s, but in the 1790s he often found himself in court facing his creditors. By the spring of 1797 he had moved to Baltimore, probably to escape his debts. Custis last appeared as a defendant in the Accomack County courthouse on October 18, 1797, and afterward disappeared from the county records. The date and place of his death are unknown. He may have been the Edmund Custis, of the city of Baltimore, who late in 1805 petitioned the Maryland House of Delegates to declare him insolvent.