The dependences of ion laser level density, gain, and output power on the parameters of hollow cathode discharge (HCD) for Hg+, Tl+ and Ga+ lasing transitions pumped due to inelastic thermal charge-transfer collisions with simultaneous excitation are studied both theoretically and experimentally. The transitions involved in these processes are 7p2P-7s 2S and 7p 2P-6d 2D Hg II in He-Hg mixture andnp 1,3P-ns 1,3S and np 1,3P-(n - 1)d1,3D Tl II (n=7) and Ga II (n=5) in the Ne-Tl mixture and Ne-Ga mixture, respectively (these mixtures are most efficient laser media for pulsed HCD lasers). A detailed kinetic model is developed based on statement that the total charge transfer rate for all pumped metal levels is equal to buffer gas ionization rate because in HCD negative glow (NG) the decay rate of the buffer gas ion by charge-transfer process is higher than that due to ambipolar diffusion. This model allows for the collisions of excited metal ions with thermal electrons and atoms that lead to ion excitation or de-excitation and uses the transition probabilities calculated in the Coulomb approximation with the account for resonance trapping. It also uses the partial charge-transfer cross sections calculated based on Landau-Zener theory and the Wigner's spin rule and corrected against the experimental data. The NG thermal electron temperature and other discharge parameters typical of HCD are calculated. The results calculated for the known laser transitions are in a good agreement with the experimental data and are used for prediction of laser parameters on new IR transitions.