Positronium (Ps) formation processes of hydrogen (H)-like ions by positron impact are investigated by employing the two-centre two-channel eikonal final state-continuum initial distorted wave model. The differential and integrated cross sections for Ps formation into the ground state are calculated for ions A (Z−1)+ with nuclear charge Z = 1-9. Comparisons with the first-order Coulomb-Born and the continuum distorted-wave final-state models are made. The differential cross sections and the Thomas double-scattering processes for H-like ions are investigated. For the integrated Ps formation cross sections, a scaling law is introduced and it is reasonably followed by H-like ions with Z 3 in the entire energy range. The maximum positions of the ground Ps formation cross sections for the H-like isoelectronic sequences are found to be in good agreement with the wave vector matching model of Charlton (2006