We report the discovery of superconductivity in noncentrosymmetric NbReSi, which crystallizes in a hexagonal ZrNiAl-type crystal structure with space group P 62m (No. 189). Bulk superconductivity, with Tc = 6.5 K was characterized via electrical-resistivity, magnetization, and heat-capacity measurements. The low-temperature electronic specific heat suggests a fully gapped superconducting state in NbReSi, while a large upper critical field of µ0Hc2(0) ∼ 12.6 T is obtained, which is comparable to the weak-coupling Pauli limit. The electronic band-structure calculations show that the density of states at the Fermi level are dominated by Re and Nb d-orbitals, with a sizeable band splitting induced by the antisymmetric spin-orbit coupling. NbReSi represents another candidate material for revealing the puzzle of time-reversal symmetry breaking observed in some Re-based superconductors and its relation to the lack of inversion symmetry.