The production of ϕ mesons has been studied in pp collisions at LHC energies with the ALICE detector via the dimuon decay channel in the rapidity region 2.5 < y< 4. Measurements of the differential cross section d 2σ/ d yd pT are presented as a function of the transverse momentum (pT) at the center-of-mass energies s=5.02, 8 and 13 TeV and compared with the ALICE results at midrapidity. The differential cross sections at s=5.02 and 13 TeV are also studied in several rapidity intervals as a function of pT, and as a function of rapidity in three pT intervals. A hardening of the pT-differential cross section with the collision energy is observed, while, for a given energy, pT spectra soften with increasing rapidity and, conversely, rapidity distributions get slightly narrower at increasing pT. The new results, complementing the published measurements at s=2.76 and 7 TeV, allow one to establish the energy dependence of ϕ meson production and to compare the measured cross sections with phenomenological models. None of the considered models manages to describe the evolution of the cross section with pT and rapidity at all the energies. © 2021, The Author(s).