We present the first experimental study of the Fermi surface of the cluster superconductor ZrB12, using the de Haas-van Alphen dHvA effect by magnetic torque measurements in magnetic fields up to 28 T at temperatures down to 0.07 K. The band structure and dHvA frequencies as well as the cyclotron effective masses were calculated using the full potential Linear Muffin-Tin Orbital method within the Generalized Gradient Approximation. We have found that the Fermi surface, FS, of ZrB12 consist from one Cu – like but hole open FS sheet and closed electron ''Cubic Box'' – like sheets. The dHvA oscillations due to orbits from the Neck sections and Cubic Box of the FS were detected, while Belly orbits were not observed. The comparison of the angular dependence of the dHvA frequencies with the band-structure calculations implies overall agreement with theoretical model. The comparison of the experimental and calculated cyclotron mass shows unusually large electron-phonon interaction on Neck (λep = 0.95) and Box (λep = 1.07) sections of the FS on the Brillouin zone boundaries. Results support observation of magnetic breakdown between Neck and Box sheets at B//<110> in fields above 25 T.