Transverse momentum spectra of direct (prompt) photons from two-body processes in high-energy proton-proton (p+p) collisions are analyzed in this paper. The experimental invariant cross-sections are collected at mid-rapidity in p+p collisions measured by the UA6, CCOR, R806, R110, PHENIX, NA24, CMS, ALICE, and ATLAS Collaborations over a center-of-mass energy range from 24.3 GeV to 13 TeV. In fitting the data, different kinds of functions are used which include the revised Tsallis-Pareto-type function (the TP-like function) at the particle level, the convolution of two TP-like functions at the quark level, and the root-sum-of-squares of two revised Tsallis-like functions in which the quark chemical potentials 𝝁 i = 𝝁 B ∕3 or 𝝁 i = 0, where 𝝁 B is the baryon chemical potential. The values of three main free parameters have been extracted: the effective temperature T, power index n 0 (or entropy index q), and correction index a 0 . After analyzing the changing trends of the parameters, it is found that T, q, and a 0 increase and n 0 decreases with the increase of collision energy. Based on the analyses of transverse momentum spectra, an energy independent scaling, that is, the x T scaling, is obtained.