Kondo effect is an interesting phenomenon in quantum many-body physics. Niobium (Nb) is a conventional superconductor important for many superconducting device applications. It was long thought that the Kondo effect cannot be observed in Nb because the magnetic moment of a magnetic impurity, e.g. iron (Fe), would have been quenched in Nb. Here we report an observation of the Kondo effect in a Nb thin film structure. We found that by co-annealing Nb films with Fe in Argon gas at above 400 ^{circ }C for an hour, one can induce a Kondo effect in Nb. The Kondo effect is more pronounced at higher annealing temperature. The temperature dependence of the resistance suggests existence of remnant superconductivity at low temperatures even though the system never becomes superconducting. We find that the Hamann theory for the Kondo resistivity gives a satisfactory fitting to the result. The Hamann analysis gives a Kondo temperature for this Nb–Fe system at sim 16 K, well above the superconducting transition onset temperature 9 K of the starting Nb film, suggesting that the screening of the impurity spins is effective to allow Cooper pairs to form at low temperatures. We suggest that the mechanism by which the Fe impurities retain partially their magnetic moment is that they are located at the grain boundaries, not fully dissolved into the bcc lattice of Nb.