We report the observation of two structures in the J/psi-phi mass spectrum of exclusive B+ -> J/psi phi K+ decays produced in pp collisions at sqrt(s) = 7 TeV using 5.2 fb-1 of integrated luminosity collected with the CMS detector at the Large Hadron Collider. Interpreting the two structures as J/psi-phi resonances with S-wave relativistic Breit-Wigner lineshapes over a three-body phase-space non-resonant component, we obtain a significance exceeding 5-sigma for the first structure. The fitted mass of the first structure is m = 4148.2 +/- 2.0(stat) +/- 4.6(syst) MeV. This observation is consistent with a previous evidence for a narrow structure near J/psi-phi threshold by the CDF Collaboration. The fitted mass of the second structure is m = 4316.7 +/- 3.0(stat) +/- 7.3(syst) MeV.