Weyl semimetals, characterized by nodal points in the bulk and Fermi arc states on the surface, have recently attracted extensive attention due to the potential application on low energy consumption electronic materials. In this report, the thermodynamic and transport properties of a theoretically predicted Weyl semimetal NbIrTe4 is measured in high magnetic fields up to 35 T and low temperatures down to 0.4 K. Remarkably, NbIrTe4 exhibits a nonsaturating transverse magnetoresistance which follows a power-law dependence in B. Low-field Hall measurements reveal that hole-like carriers dominate the transport for T $>$ 80 K, while the significant enhancement of electron mobilities with lowering T results in a non-negligible contribution from electron-like carriers which is responsible for the observed non-linear Hall resistivity at low T. The Shubnikov-de Haas oscillations of the Hall resistivity under high B give the light effective masses of charge carriers and the nontrivial Berry phase associated with Weyl fermions. Further first-principles calculations confirm the existence of 16 Weyl points located at kz = 0, $pm$0.02 and $pm$0.2 planes in the Brillouin zone.
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