We report the discovery of an additional substellar companion in the CoRoT-20 system based on six years of HARPS and SOPHIE radial velocity follow-up. CoRoT-20 c has a minimum mass of 17 ± 1 M_Jup and orbits the host star in 4.59 ± 0.05 yr, with an orbital eccentricity of 0.60 ± 0.03. This is the first identified system with an eccentric hot Jupiter and an eccentric massive companion. The discovery of the latter might be an indication of the migration mechanism of the hot Jupiter, via the Lidov–Kozai effect. We explore the parameter space to determine which configurations would trigger this type of interactions.