Eric was the only son of the Duke Albert I of Brunswick-Grubenhagen, who died in 1383, and his wife Agnes I, a daughter of Duke Magnus II of Brunswick-Lüneburg. Eric inherited Brunswick-Grubenhagen at a very early age; he stood until 1401 under the guardianship of his uncle, Duke Frederick of Grubenhagen-Osterode. From 1402 they joined ruled the principality and Eric moved his residence to Salzderhelden.

Disputes arose with his cousins Bernard I and Frederick I of Lüneburg, with the city of Brunswick, with his former guardian, with the counts of Schwarzburg and the Landgrave of Thuringia. All these disputes were soon settled again.

In 1406 Eric was captured in a feud with the Lords of Hardenberg in Lindau. He was only released after he gave them a written Urfehde and the city of Osterode am Harz as collateral.

In 1415, Eric declared war on the Counts of Hohenstein, because both sides claimed the county of Bad Lauterberg im Harz and defeated them near the village of Osterhagen. Count Guenther of Hohenstein died during the battle; Counts Henry and Ernest were captured and had to pay 8000 florins and renounce their claims to redeem themselves.

A dispute with the Lords of Bortfeld was settled soon after Eric entered into an alliance against them with the City of Brunswick. A dispute with Landgrave Frederick "the Peaceful" of Thuringia about the city of Einbeck was also settled quickly.

In 1422, the Abbess of Gandersheim Abbey (who happened to be his daughter, Agnes II of Brunswick-Grubenhagen) enfeoffed him with castle and city of Elbingerode. Two years, in 1424, the Abbess of Quedlinburg Abbey (Countess Adelheid of Isenburg), enfeoffed the Dukes of Grubenhagen with Duderstadt, Gieboldehausen and the Golden Mark.

Eric was married to Elisabeth, a daughter of Duke Otto I, Duke of Brunswick-Göttingen (referred to as "Otto The Mad" or "Otto The Evil"). They had three sons and five daughters, including:

• Agnes (1406–1439), Abbess of Gandersheim Abbey
• Margaret (1411 – 31 October 1456) married Simon IV, Lord of Lippe in 1426
• Anna (1414–1474) married first to Albert III, Duke of Bavaria and later to Frederick III, Duke of Brunswick-Göttingen-Calenberg
• Henry III (1416–1464), who succeeded his father
• Ernest II (1418–1466), who became provost of the St. Alexandri minster in Einbeck
• Albert II (1419–1485), who succeeded his father
• Elisabeth of Brunswick-Grubenhagen, who married Casimir V, Duke of Pomerania.

• Ferdinand Spehr (1877), "Erich I., Herzog von Braunschweig-Grubenhagen", Allgemeine Deutsche Biographie (in German), vol. 6, Leipzig: Duncker & Humblot, pp. 201–202