Single-electron capture from the K shell of atomic targets by impact of protons at moderate and high energies has been studied using a first-order three-body Coulomb-Born continuum distorted wave approximation. The applied formalism satisfies the correct Coulomb boundary conditions. Single-zeta Roothaan-Hartree-Fock wave functions are used to describe the initial electronic bound state of the exchanged electron. Both differential and integral capture cross sections are calculated for impact of protons on carbon, nitrogen, oxygen, neon and argon atoms. The results are compared with the available measurements and other theories. The agreement between the calculations and experimental data is remarkable.