Dunstaple was probably born in Dunstable, Bedfordshire. His birth date is a conjecture based on his earliest surviving works (from around 1410–1420) which imply a birth date of around 1390. Many of the details of his life are conjectural. Nothing is known of his musical training and background. He was clearly a highly educated man, though there is no record of an association with either Oxford or Cambridge universities. He is widely held to have been in the royal service of John of Lancaster, 1st Duke of Bedford, the fourth son of Henry IV and brother of Henry V. As such he may have stayed in France for some time, since the duke was Regent of France from 1423 to 1429, and then Governor of Normandy from 1429 to his death in 1435. He owned property in Normandy, and also in Cambridgeshire, Essex and London, according to tax records of 1436. After the death in 1437 of another patron, the Dowager Queen Joan, he evidently was in the service of Humphrey, Duke of Gloucester, the fifth son of Henry IV.
Unlike many composers of the time, he was probably not a cleric, though there are links with St Albans Abbey (see below); he was probably married, based on the record of women sharing his name in his parish, and he also owned a manor in Hertfordshire.
In addition to his work as a composer, he had a contemporary reputation as an astronomer, astrologer, and mathematician (for example, a volume in the Bodleian Library, largely in the hand of William Worcester, acknowledges that certain information within it had been copied from Dunstaple's writings). Some of his astrological works have survived in manuscript, possibly in his own hand.[