Type Ia supernovae are thought to result from thermonuclear explosions of carbon-oxygen white dwarf stars. Existing models generally explain the observed properties, with the exception of the sub-luminous 1991bg-like supernovae. It has long been suspected that the merger of two white dwarfs could give rise to a type Ia event, but hitherto simulations have failed to produce an explosion. Here we report a simulation of the merger of two equal-mass white dwarfs that leads to a sub-luminous explosion, although at the expense of requiring a single common-envelope phase, and component masses of approximately 0.9M[symbol: see text]. The light curve is too broad, but the synthesized spectra, red colour and low expansion velocities are all close to what is observed for sub-luminous 1991bg-like events. Although the mass ratios can be slightly less than one and still produce a sub-luminous event, the masses have to be in the range 0.83M[symbol: see text] to 0.9M[symbol: see text].