Henry was the eldest son of Eric I, Duke of Brunswick-Grubenhagen and Elizabeth of Brunswick-Göttingen, a daughter of Otto the Bad, Duke of Brunswick-Göttingen. After the death of his father in 1427, he ruled jointly with his younger brothers Ernest II and Albert II.

Until his coming of age in 1437 he was under the guardianship of Duke Otto II of Brunswick-Grubenhagen-Osterode. In the year 1447 a feud broke out between Henry and Louis I, Landgrave of Hesse, who was allied with the Archbishop of Mainz and the dukes of Göttingen. Louis and his allies besieged Grubenhagen Castle, but despite the deployment of two cannon, had to withdraw again. Even an attack on Salzderhelden was unsuccessful. Henry died in 1464 and was interred in the Alexanderstift in Einbeck. He was followed by his son, Henry.

Henry married Margaret of Sagan (1415/25 – 9 May 1497), the daughter of John I, Duke of Sagan, and Scholastika of Saxe-Wittenberg before 27 June 1457. He was her third husband. They had two sons:^{[citation needed]}

• Otto (b. 1458; d. as child)
• Henry IV (1460–1526) married Elisabeth of Saxe-Lauenburg (d after 7 April 1542), daughter of Duke John V of Saxe-Lauenburg.

• Ludwig Ferdinand Spehr (1880), "Heinrich III., Herzog von Braunschweig-Grubenhagen", Allgemeine Deutsche Biographie (in German), vol. 11, Leipzig: Duncker & Humblot, pp. 488–489