We surveyed the 25 Ori association for direct-imaging companions. This association has an age of only few million years. Among other targets, we observed CVSO 30, which has recently been identified as the first T Tauri star found to host a transiting planet candidate. We report on photometric and spectroscopic high-contrast observations with the Very Large Telescope, the Keck telescopes, and the Calar Alto observatory. They reveal a directly imaged planet candidate close to the young M3 star CVSO 30. The JHK-band photometry of the newly identified candidate is at better than 1 sigma consistent with late-type giants, early-T and early-M dwarfs, and free-floating planets. Other hypotheses such as galaxies can be excluded at more than 3.5 sigma. A lucky imaging z photometric detection limit z= 20.5 mag excludes early-M dwarfs and results in less than 10 MJup for CVSO 30 c if bound. We present spectroscopic observations of the wide companion that imply that the only remaining explanation for the object is that it is the first very young (< 10 Myr) L-T-type planet bound to a star, meaning that it appears bluer than expected as a result of a decreasing cloud opacity at low effective temperatures. Only a planetary spectral model is consistent with the spectroscopy, and we deduce a best-fit mass of 4-5 Jupiter masses (total range 0.6-10.2 Jupiter masses). This means that CVSO 30 is the first system in which both a close-in and a wide planet candidate are found to have a common host star. The orbits of the two possible planets could not be more different: they have orbital periods of 10.76 hours and about 27000 years. The two orbits may have formed during a mutual catastrophic event of planet-planet scattering.