A multi-ion kinetic model for a coronal loop is presented, whereby ion heating in the magnetically confined plasma is achieved by absorption of ion-cyclotron waves. We assume that linear Alfven/cyclotron waves penetrate the loop from its footpoint and directly heat the ions. Then due to electron-ion collisions the electrons can also be heated. Depending on the spatial variation of the mean magnetic field, the model is able to produce warm and hot model loops having features similar to the ones observed in extreme-ultraviolet and soft X-ray emissions in real coronal loops. Furthermore, it is found that a loop with high expansion factor is far from local thermal equilibrium (LTE) and shows remarkable temperature differences between electrons and ions. Also in such a case, the heavy ions (minor ions) are via resonant wave absorption heated more than the protons and helium ions (major background ions), whereby the cyclotron-resonance effect leads to a temperature anisotropy with T⊥ > T∥. However, if the flux tube cross section is nearly homogeneous, temperature isotropy of the ions is maintained in most parts of the loop, and the plasma is nearly in LTE.