Ralph was the son on Sir Henry Greene, who was executed in Bristol Castle by the Duke of Hereford (soon to be Henry IV of England) for treason, and Maud (or Matilda) Mauduit
Ralph married Katherine Clifton, daughter of John, Lord Clifton of Buckenham, Norf and Elizabeth Cromwell, daughter of Ralph, 1st Lord Cromwell.
Sheriff, Northants. 29 Oct. 1404-22 Nov. 1405, 23 Nov. 1407-15 Nov. 1408, 10 Nov. 1414-1 Dec. 1415, Wilts. 5 Nov. 1406-30 Nov. 1407.
J.p. Wilts. 13 Feb. 1410-12, Northants. 16 Nov. 1413-d.
Commr. to hold special assizes, Northants. Easter 1410 (dispute over the ownership of the manor of Hinton by Brackley),2 July 1414 (ownership of land in Drayton); of inquiry June 1413 (felonies and trespasses), July 1414 (dispute over common pasture at Byfield), Mar. 1416 (holdings of Edmund, earl of Stafford); to make arrests, generally June 1413, Northants. Jan. 1414 (lollards at large), generally Feb. 1414 (bis); of oyer and terminer, Lincs. May 1415 (assault on Croyland abbey), Beds. July 1416 (disorder at the manor of Ampthill).
Escheator, Northants. and Rutland 10 Nov. 1413-12 Nov. 1414.
Survevor and keeper of the royal park of Brigstock, Northants. 12 Mar. 1416-d.