After 1413, George married Matilda (d. Coswig, bef. 1432), daughter of Otto III, Prince of Anhalt-Bernburg. The spouses were related to each other as direct descendants of Henry I, Count of Anhalt, through his sons Bernhard I of Anhalt-Bernburg (ancestor of Matilda), and Siegfried I of Anhalt-Zerbst (ancestor of George). The marriage was childless.
In 1432 George married for a second time to Euphemia (b. ca. 1404? - d. 27 November 1442), daughter of Konrad III the Old, Duke of Oleśnica and widow of Albert III, Elector of Saxony. They had six daughters:
- Anna (d. 8 April 1492), married on 22 June 1461 to Henry II, Count of Plauen and Burgrave of Meissen (later were divorced), then for a second time in 1467 to John I, Count of Honstein-Heldrungen
- Margarete (d. bef. 1516)
- Hedwig (d. young)
- Marie, nun at Brehna
- Hedwig (d. bef. 1516), nun at Brehna
- Barbara, nun at Brehna.
After 1442, George married for a third time to Sophie (d. 1451), possibly a member of the House of Hohnstein. They had three children:
- Agnes (b. 1445 – d. Kaufungen, 15 August 1504), Abbess of Gandersheim (1485), of Neuenheerse (1486–1492) and of Kaufungen (1495)
- Waldemar VI, Prince of Anhalt-Köthen (b. 1450 – Köthen, 1 November 1508)
- Scholastica [de] (b. 1451 – d. Gernrode, 31 July 1504), Abbess of Gernrode (1469).
On 7 September 1453 George married for a fourth time to Anna (b. ca. 1430 – d. Lippehne, 9 July 1513), daughter of Albert VIII, Count of Lindow-Ruppin and his wife Anna of Sagan (d. of Jan I of Żagań). They had nine children:
- Ernest I, Prince of Anhalt-Dessau (d. Dessau, 12 June 1516)
- George II, Prince of Anhalt-Dessau (b. 1454 – d. 25 April 1509)
- Sigismund III, Prince of Anhalt-Dessau (d. 1456 – d. Dessau, 27 November 1487)
- Anna (d. 10 October 1531), married on 20 June 1498 to John V, Count of Oldenburg-Delmenhorst
- Rudolph IV, Prince of Anhalt-Dessau (d. 7 September 1510)
- Bernhard (d. young)
- John (d. young)
- Henry (d. young)
- Lorenz (d. young).