Hopper was born Grace Brewster Murray in New York City. For her prep school education, she attended the Hartridge School in Plainfield, NJ. She

In 1943 she joined the U.S. Naval Reserve on active duty and was assigned to work with Howard Aiken on the Mark I Calculator. At the end of the war she was separated from active duty with the Navy, remaining in the reserves, but she continued to work on the development of the Mark II and the Mark III calculators (early computers). It was while she was working on Mark II that technicians discovered a moth in a relay — a bug in the computer. Hopper pasted it into a log book (now in the National Museum of American History at the Smithsonian Institution), noting it as the first actual case of a bug being found. Erroneously, some have cited this incident as the genesis of the term bug, but the term was already in wide use.

In 1949, Hopper became an employee of the Eckert-Mauchly Computer Corporation and joined the team developing the UNIVAC I. In the early 1950s the company was taken over by the Remington Rand corporation and it was while she was working for them that her original compiler work was done. The compiler was known as the A compiler and its first version was A-0. Later versions were released commercially as the ARITH-MATIC, MATH-MATIC and FLOW-MATIC compilers.

She later returned to the Navy where she worked on validation software for the programming language COBOL and its compiler. COBOL was defined by the CODASYL committee

Hopper was a pioneer in the field of computer science. She was one of the first programmers of the Harvard Mark I calculator, and she developed the first compiler for a computer programming language. Because of the breadth of her accomplishments and her naval rank, she is sometimes referred to as "Amazing Grace".

It was her idea that programs could be written in a language that was close to English rather than in machine code or languages close to machine code (such as assembly language), which is how it was normally done at that time.

Hopper retired from the Naval Reserve with the rank of Commander at the end of 1966. She was recalled to active duty in August of 1967 for a six-month period that turned into an indefinite assignment. She again retired in 1971 but was asked to return to active duty again in 1972. She was promoted to Captain in 1973 by Admiral Elmo R. Zumwalt, Jr..

After Rep. Philip Crane saw her on a March 1983 segment of 60 Minutes, he championed H.J.RES.341 a joint resolution in the House of Representatives which led to her promotion to Commodore by special Presidential appointment.[6] In 1985, the rank of Commodore was renamed Rear Admiral, Lower Half. She retired (involuntarily) from the Navy on August 14, 1986. At a celebration held in Boston on the USS Constitution to celebrate her retirement, Hopper was awarded the Defense Distinguished Service Medal, the highest non-combat award possible by the Department of Defense. At the moment of her retirement, she was the oldest officer in the U.S. Navy and aboard the oldest ship in the U.S. Navy.

She was then hired as a senior consultant to Digital Equipment Corporation, a position she retained until her death in 1992, aged 85.

Her primary activity in this capacity was as a Goodwill Ambassador, lecturing widely on the early days of computers, her career, and on efforts that computer vendors could take to make life easier for their users. She visited a large fraction of Digital's engineering facilities where she generally received a standing ovation at the conclusion of her remarks. She always wore her Navy full dress uniform to these lectures.