A search for low-mass structures in the J/psiJ/psi mass spectrum produced by proton-proton collisions at sqrt(s) = 13 TeV is performed at the CMS experiment. The data sample corresponds to an integrated luminosity of 135 fb^-1 collected by the CMS at the CERN LHC. The previously observed X(6900) by LHCb is confirmed in this study, and a new structure at a lower mass is observed. Both structures have a significance well above 5 standard deviations. Evidence for a third structure around 7.2 GeV is found with a local significance of 4 sigma.