We report four narrow peaks in the mass spectrum obtained using collisions at center-of-mass energies of 7, 8, and 13 TeV, corresponding to a total integrated luminosity of recorded by the LHCb experiment. Referring to these states by their mass, the mass values are m[Ωb(6316)-]=6315.64±0.31±0.07±0.50  MeV, m[Ωb(6330)-]=6330.30±0.28±0.07±0.50  MeV, m[Ωb(6340)-]=6339.71±0.26±0.05±0.50  MeV, m[Ωb(6350)-]=6349.88±0.35±0.05±0.50  MeV, where the uncertainties are statistical, systematic, and the last is due to the knowledge of the mass. The natural widths of the three lower mass states are consistent with zero, and the 90% confidence-level upper limits are determined to be , and . The natural width of the peak is , which is from zero and corresponds to an upper limit of 2.8 MeV. The peaks have local significances ranging from to . After accounting for the look-elsewhere effect, the significances of the and peaks are reduced to and , respectively, while the two higher mass peaks exceed . The observed peaks are consistent with expectations for excited resonances.