Born in Angola to missionary parents, Dodson grew up in Southern California and worked for the U.S. Merchant Marine, mainly the American Mail Line, from 1925 to 1942. From November 1942 he served in the U.S. Navy, chiefly on the attack transport USS Pierce, in invasions in the Central and South Pacific. Wounded in these battles, he retired from the active Navy in 1947. From 1948 to 1952 he studied creative writing under George Savage at the University of Washington. He wrote a thinly disguised novel of his wartime naval experiences and received editing suggestions from Carl Sandburg, who had used some of Dodson's combat letters in his 1947 novel. Dodson's Away All Boats finally was published by Little Brown in 1954, quickly made the best seller lists, was published in foreign editions, and sold well for at least ten years. His next novel, Stranger to the Shore, set in a small Chilean port, was published in 1956 but proved less successful. In 1956 he also wrote a story, Hector the Stowaway Dog, for Reader's Digest and subsequently expanded it to a full length children's book, published in 1958. In 1960 Little Brown published his novel, China Pirates. Some of his shorter pieces were published in anthologies and magazines. A movie of Away All Boats was made by Universal-International with cooperation of the U.S. Navy. Walt Disney also made a children's movie of Hector the Stowaway Dog.

Dodson and his family lived north of Seattle near Anacortes but spent a year in Hawaii in 1955. There Dodson worked on a nonfiction account of the life of a pure blooded Hawaiian mother. Titled Hawaii's Wreath of Love, it was not published. In the early 1970s Dodson assisted his minister friend Bill Roberts with an autobiography, From Make-Believe to Reality, published in 1973 with Dodson as author.

Dodson maintained a long correspondence with his parents, William and Catherine Dodson, with his wife Oletha while he was at sea, and with many family members and friends. He died in 1999.