Only a quarter of the approximately 200 original machines are thought still to exist. In 1977 Apple encouraged buyers to trade in the computer for the next model at a discount, and destroyed many of the recovered Apple-1s.
Christie's expect the Apple-1, which comes with a rare first manual, to fetch between £300,000 and £500,000.
The Apple-1 was designed and hand-built by Steve Wozniak, who co-founded Apple with Steve Jobs. The two are portrayed in Steve Jobs, a new film by Danny Boyle released in November.
The Apple-1 appears in Christie's 'Seven Centuries of Science' online timed sale from October 15-29.