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Here we present a study of the Shubnikov-de Haas (SdH) effect in the type-II Weyl semimetal candidate NbIrTe₄. Quantum oscillations were obtained at temperatures down to 0.3 K and in high magnetic fields up to 35 T. The angular dependence of the SdH frequencies is in good agreement with results from DFT calculations, although we are not able to detect every orbit. We observe an unusual butterfly shaped magnetoresistance as a function of the sample orientation with respect to the magnetic field, which is likely to originate from the shape and anisotropy of the Fermi surface. Furthermore, we measured a large non-saturating magnetoresistance up to fields 35 T which suggests charge carrier compensation. On the other hand Hall measurements indicate significantly different electron and hole densities, which implies that the non-saturating magnetoresistance is not driven by charge carrier compensation.