He was born in Amsterdam in a rich merchant family - his father, Reinier Pauw (1564–1636) wasn't only a merchant, but also a Mayor of Amsterdam - and studied law in Leiden. He was the pensionary of Amsterdam from 1611 to 1627. In 1620 he bought the town of Heemstede and was called 'Lord of Heemstede'. He was appointed grand pensionary in 1631. Pauw, Holland and Amsterdam wanted an alliance with Spain, but Prince Frederick Henry of Orange wanted an alliance with France. Frederick Henry sent Pauw to France to start an alliance against Spain. Pauw accepted this assignment and allied with France. He resigned in 1636 as grand pensionary. After the Peace of Münster (1648) for which he was instrumental as ambassador for Holland Pauw became grand pensionary again in 1651 although there was much opposition against him. He tried to stop a war with England in 1652. He died in 1653.
Adriaan Pauw was married to Anna van Ruytenburgh (1589–1648), daughter of Pieter van Ruytenburgh, heer van Vlaardingen, Vlaardingerambacht en Ter Horst (1562–1627), a wealthy merchant. Her mother was Aleyda Huybrechts van Duyvendrecht.
- H. W. J. de Boer, H.Bruch, H. Krol (edit.). Adriaan Pauw (1585–1653); staatsman en ambachtsheer. Heemstede, 1985.
- J. C. Tjessinga. Schets van het leven van Adriaan Pauw. Heemstede, 1948.
- J. C. Tjessinga. Het slot van Heemstede onder Adriaan Pauw. Heemstede, 1949.