Planets orbiting post-common envelope binaries provide fundamental information on planet formation and evolution, especially for the yet nearly unexplored class of circumbinary planets. We searched for such planets in DP Leo, an eclipsing short-period binary, which shows long-term eclipse-time variations. Using published, reanalysed, and new mid-eclipse times of the white dwarf in DP Leo, obtained between 1979 and 2010, we find agreement with the light-travel-time effect produced by a third body in an elliptical orbit. In particular, the measured binary period in 2009/2010 and the implied radial velocity coincide with the values predicted for the motion of the binary and the third body around the common center of mass. The orbital period, semi-major axis, and eccentricity of the third body are P c = 28.0 ± 2.0 yrs, a c = 8.2 ± 0.4 AU, and e c = 0.39 ± 0.13. Its mass of sin i c M c = 6.1 ± 0.5 M Jup qualifies it as a giant planet. It formed either as a first generation object in a protoplanetary disk around the original binary or as a second generation object in a disk formed in the common envelope shed by the progenitor of the white dwarf. Even a third generation origin in matter lost from the present accreting binary can not be entirely excluded. We searched for, but found no evidence for a fourth body.