A planet with a minimum mass of 0.84 Jupiter masses (MJ) has been indirectly detected in a close orbit (radius 0.11 astronomical units, period 14.65 days) around the star 55 Cancri, which is of spectral type G8 and about 3 billion years old. The detection of excess infrared emission from this system also suggests the presence of circumstellar dust. Our Solar System has a disk of dust (and larger bodies) that is roughly coplanar with the planets-the so-called Kuiper Belt. Here we report infrared coronagraphic observations of 55 Cancri in which the light from the primary star is blocked, allowing us to image a circumstellar dust disk. We find that the dust lies in a disk that extends to at least 40AU, comparable to the expected extent for our Kuiper Belt, whereas the inferred mass of the disk is approximately ten times that estimated for our Kuiper Belt. The disk around 55 Cancri is relatively dark at a wavelength of 2.3µm, which is consistent with absorption of light by methane ice on the dust particles. Assuming that the disk is coplanar with the planet, we determine the planet's mass to be 1.9-0.4+1.1 Jupiter masses. All the available evidence is suggestive of a mature planetary system around 55 Cancri.