Born in Brighton, a suburb of Melbourne, to John and Annie Deas Grieve (née Brown), Grieve was educated at Caulfield Grammar School and then Wesley College. He became an interstate commercial traveller in the softgoods trade.  After nine months service in the Victorian Rangers, he enlisted in the Australian Imperial Force as a private on 9 June 1915. He was commissioned as a second lieutenant in the 37th Battalion in January 1916, was promoted to lieutenant in May 1916, and after training in England, was promoted to captain in France in February 1917.  In France he served at Armentières, Bois-Grenier, L'Epinette, Ploegsteert Wood, Messines, La Basse Ville, and Warneton.

Citation

“On 7 June 1917 at Messines, Belgium, during an attack on the enemy's position, and after his own company had suffered very heavy casualties, Captain Grieve located two hostile machine-guns which were holding up his advance. Under continuous heavy fire from the two guns, he succeeded in bombing and killing the two gun crews, then reorganized the remnants of his own company and gained his original objective. Captain Grieve set a splendid example and when he finally fell, wounded, the position had been secured.”

Severely wounded in the shoulder by a sniper's bullet, Grieve was evacuated to England, and on recovery returned to his unit in October. However, due to subsequently suffering acute trench nephritis and double pneumonia, he was invalided to Australia in May 1918. On 7 August, at Scots Church, Sydney, he married Sister May Isabel Bowman of the Australian Army Nursing Service who had nursed him during his illness.

Post-war he held the rank of captain in the Militia. He established the business of Grieve, Gardner & Co., soft-goods warehousemen, in Flinders Lane, Melbourne, and was managing director until 4 October 1957 when he died of cardiac failure.  He was buried with military honours in Springvale cemetery. Grieve's medal was presented by his family to Wesley College in 1959, and has been lent to the Shrine of Remembrance, where it is on permanent display. Grieve was an active supporter of Wesley College for many years and contributed towards an annual scholarship.