He was born in Stavanger as a son of shipmaster Johan Rasmussen (1843–1891) and Caroline Kannik (1843–1932).
[1][2] Rasmussen finished his secondary education in 1896 and graduated from the Royal Frederick University with the cand.jur.
From 1908 to 1912 he represented a large Swedish bank, and was also chief executive of Holms Hattefabrik.
Rasmussen also owned the ship holding company Rosshavet with Magnus Konow.
[3] He was a board member of Framnæs mekaniske Værksted from 1915, chaired the Den norske Hvalfangerforening from 1918 to 1929 and the whalers' insurance company Hvalfangernes Assuranceforening.