Conrad I was the fourth of six children of Margrave John I of Brandenburg and his wife Sophia, daughter of King Valdemar II of Denmark.
He was 26 years old when, in 1266, his father died and he and his elder brothers John II and Otto IV became co-rulers of Brandenburg.
Conrad went on to rule in the newly acquired Neumark part of Brandenburg east of the Oder River, though he rarely appeared on the political scene.
On one occasion, he assisted his brother Otto IV, when they allied with Duke Mestwin II of Pomerelia according to the 1269 Treaty of Arnswalde, occupying the Pomerelian city of Gdańsk and gaining the Pomeranian territory around Rügenwalde.
and was buried here.Conrad was married to Constance of Poznań (d. 1281), daughter of the Piast duke Przemysł I of Greater Poland.