The production of π ± , K ± , K S 0 , K ∗ ( 892 ) 0 , p , ϕ ( 1020 ) , Λ , Ξ - , Ω - , and their antiparticles was measured in inelastic proton–proton (pp) collisions at a center-of-mass energy of s = 13 TeV at midrapidity ( | y | < 0.5 ) as a function of transverse momentum ( p T ) using the ALICE detector at the CERN LHC. Furthermore, the single-particle p T distributions of K S 0 , Λ , and Λ ¯ in inelastic pp collisions at s = 7  TeV are reported here for the first time. The p T distributions are studied at midrapidity within the transverse momentum range 0 ≤ p T ≤ 20 GeV/ c , depending on the particle species. The p T spectra, integrated yields, and particle yield ratios are discussed as a function of collision energy and compared with measurements at lower s and with results from various general-purpose QCD-inspired Monte Carlo models. A hardening of the spectra at high p T with increasing collision energy is observed, which is similar for all particle species under study. The transverse mass and x T ≡ 2 p T / s scaling properties of hadron production are also studied. As the collision energy increases from s = 7–13 TeV, the yields of non- and single-strange hadrons normalized to the pion yields remain approximately constant as a function of s , while ratios for multi-strange hadrons indicate enhancements. The p T -differential cross sections of π ± , K ± and p ( p ¯ ) are compared with next-to-leading order perturbative QCD calculations, which are found to overestimate the cross sections for π ± and p ( p ¯ ) at high p T .