Abstract The production of $$\phi $$ ϕ mesons has been studied in pp collisions at LHC energies with the ALICE detector via the dimuon decay channel in the rapidity region $$2.5< y < 4$$ 2.5 < y < 4 . Measurements of the differential cross section $$\mathrm{d}^2\sigma /\mathrm{d}y \mathrm{d}p_{\mathrm {T}}$$ d 2 σ / d y d p T are presented as a function of the transverse momentum ( $$p_{\mathrm {T}}$$ p T ) at the center-of-mass energies $$\sqrt{s}=5.02$$ s = 5.02 , 8 and 13 TeV and compared with the ALICE results at midrapidity. The differential cross sections at $$\sqrt{s}=5.02$$ s = 5.02 and 13 TeV are also studied in several rapidity intervals as a function of $$p_{\mathrm {T}}$$ p T , and as a function of rapidity in three $$p_{\mathrm {T}}$$ p T intervals. A hardening of the $$p_{\mathrm {T}}$$ p T -differential cross section with the collision energy is observed, while, for a given energy, $$p_{\mathrm {T}}$$ p T spectra soften with increasing rapidity and, conversely, rapidity distributions get slightly narrower at increasing $$p_{\mathrm {T}}$$ p T . The new results, complementing the published measurements at $$\sqrt{s}=2.76$$ s = 2.76 and 7 TeV, allow one to establish the energy dependence of $$\phi $$ 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 $$p_{\mathrm {T}}$$ p T and rapidity at all the energies.