A search for new resonances decaying into jets containing b-hadrons in pp collisions with the ATLAS detector at the LHC is presented in the dijet mass range from 0.57 to 7 TeV. The data set corresponds to an integrated luminosity of up to 36.1 fb-1 collected in 2015 and 2016 at s=13 TeV. No evidence of a significant excess of events above the smooth background shape is found. Upper cross-section limits and lower limits on the corresponding signal mass parameters for several types of signal hypotheses are provided at 95% C.L. In addition, 95% C.L. upper limits are set on the cross sections for new processes that would produce Gaussian-shaped signals in the di-b-jet mass distributions.