Electromagnetic ion cyclotron (EMIC) waves are excited near the magnetic equator by anisotropic ring current ions with energies near a few tens of keV. We investigate the instability and the path‐integrated gain of EMIC waves during wave propagation. Calculations are performed by a global core density model, a field‐aligned density model and particularly the hot ring current ions modeled by a kappa distribution. Simulating results show that the instability of EMIC waves is influenced primarily by the parameters of hot ring current ions, the wave normal angle and the composition of background plasma. A larger path‐integrated gain occurs when the initial wave vector points toward lower L shells. During the storm main phase, the most common EMIC wave is the He+ band wave which occurs in the outer magnetosphere beyond the plasmapause with frequency just below the cyclotron frequency of He+. During the recovery phase, EMIC wave occurs in H+ band and He+ band with almost the same intensity in cases of interest. The O+ band EMIC waves are very weak and quite rare. This result presents a further insight into propagation and instability of EMIC waves under different geomagnetic activities.