The decay J/ψ→γγφ is studied using a sample of 1.31×109 J/ψ events collected with the BESIII detector. Two structures around 1475 MeV/c2 and 1835 MeV/c2 are observed in the γφ invariant mass spectrum for the first time. With a fit on the γφ invariant mass, which takes into account the interference between the two structures, and a simple analysis of the angular distribution, the structure around 1475 MeV/c2 is found to favor an assignment as the η(1475) and the mass and width for the structure around 1835 MeV/c2 are consistent with the X(1835). The statistical significances of the two structures are 13.5σ and 6.3σ, respectively. The results indicate that both η(1475) and X(1835) contain a sizeable ss component.