Multi-century sea-level records and climate models indicate an acceleration of sea-level rise, but no 20th century acceleration has previously been detected. A reconstruction of global sea level using tide-gauge data from 1950 to 2000 indicates a larger rate of rise after 1993 and other periods of rapid sea-level rise but no significant acceleration over this period. Here, we extend the reconstruction of global mean sea level back to 1870 and find a sea-level rise from January 1870 to December 2004 of 195 mm, a 20th century rate of sea-level rise of 1.7 ± 0.3 mm yr−1 and a significant acceleration of sea-level rise of 0.013 ± 0.006 mm yr−2. This acceleration is an important confirmation of climate change simulations which show an acceleration not previously observed. If this acceleration remained constant then the 1990 to 2100 rise would range from 280 to 340 mm, consistent with projections in the IPCC TAR.