John was born in Geelong and his father was Rev J W Grove who later became Headmaster of the Methodist Ladies College, Melbourne. He was educated at several schools in Victoria, Tasmania and Western Australia. After leaving school in Western Australia he became apprenticed to a pharmacist in Perth. However, he did not finish his apprenticeship as he won a scholarship and commenced a medical course at the Melbourne University. He graduated in 1929 obtaining honours each year. He was at the Womens' Hospital in Melbourne when he obtained his MD in 1931. In 1932 he was appointed Medical Superintendent of the Launceston General Hospital, a position which he occupied until 1936 when he left the Hospital to enter private practice. He was appointed an honorary in-patient physician at the Launceston General Hospital in 1937, a position held until his retirement from the Institution in 1963. During the severe polio epidemic from 1937 to 1938 he was appointed chairman to the Tasmanian Poliomyelitis Advisory Committee.

He became a foundation fellow of the College in 1938. During the World War II war he was part-time CO of the 110 Convalescent Depot and Consulting Physician to the 111th Australian General Hospital. During his career he held the position of Consultant Physician to the Devon Hospital, Latrobe, as well as to the Burnie Public Hospital. He was in addition, the Consultant Physician for the Repatriation Department in Tasmania and was a referee for the Workers Occupational Disease Board of Tasmania. Having been a member of the Launceston General Hospital Board since 1944 he was appointed chairman in 1950 and served in that position until 1960.

John was particularly interested in diseases of the thyroid gland and was one of the early users of radioactive iodine in the treatment of thyroid diseases. His work led to the development of the hospital nuclear medicine department. He retired from private practice in 1972 when he took up the position of geriatrician to the Cosgrove Park Home, Launceston General Hospital from 1972 to 1978. He was an active member of The College Tasmanian State Committee and being on the Committee from 1938 to 44, 1950 to 58, 1962 to 66, was Chairman of the Committee from 1941 to 43. He was co-opted Councillor in 1963 to 65 and Australasian Annals of Medicine editorial representative from 1951 onwards.

He took an active part in Medico Politics and was on the Tasmanian Branch Council of the BMA for a number of years. He was one of the Tasmanian Representatives of the Federal Council of the BMA for several years and was President of the Tasmanian Branch of the BMA in 1947. He was elected a Fellow of the AMA in 1965. In addition he took a great deal of interest in St. John Ambulance and in the early days was a Divisional Surgeon. Later he became a Member of the State Council of St. John and was promoted to the position of commander. In 1960 he became a Member of the Tasmanian Section of the Royal Flying Doctor Service of Australia being one of the prime movers in its establishment in Tasmania. He was an active councillor at the time of his passing. For some years he was a Member of the Federal Council of the Service and from 1970 to 73 he was the Federal President. He was made an Honorary Life Member of the Tasmanian Section in 1987.

He was a dedicated Rotarian joining the Launceston Rotary Club in 1937. He was Club President in 1954 to 55 and later was appointed District Governor in 1971 to 72. He was a regular attender at the Club right up to the time of his demise. He possessed a phenomenal memory, was a classics scholar and completely dedicated to any cause he espoused, and was a man of proven judgement. His death on the 29th June, 1990, was a severe loss to the profession and the community, and his knowledge and understanding has been sadly missed. He married Helen Rex on 10th January, 1934. They had three sons, Captain James Grove (Merchant Marine), Dr. John Rex Grove (FRCOG), Captain Donald Grove (Merchant Marine).