The branching fraction of the decay B + → ψ ( 2 S ) ϕ ( 1020 ) K + , relative to the topologically similar decay B + → J / ψ ϕ ( 1020 ) K + , is measured using proton-proton collision data collected by the LHCb experiment at center-of-mass energies of 7, 8, and 13 TeV, corresponding to an integrated luminosity of 9 fb − 1 . The ratio is found to be 0.061 ± 0.004 ± 0.009 , where the first uncertainty is statistical and the second systematic. Using the world-average branching fraction for B + → J / ψ ϕ ( 1020 ) K + , the branching fraction for the decay B + → ψ ( 2 S ) ϕ ( 1020 ) K + is found to be ( 3.0 ± 0.2 ± 0.5 ± 0.2 ) × 10 − 6 , where the first uncertainty is statistical, the second systematic, and the third is due to the branching fraction of the normalization channel.