A firing rate (FR) model for a population of adaptive integrate-and-fire (IF) neurons has been proposed. Unlike known FR models, it describes more precisely the unsteady firing regimes and takes into account the effect of slow potassium currents of spike-time adaptation. Approximations of the adaptive channel conductances are rewritten from voltage-dependent to spike-dependent and then to rate-dependent ones. The proposed FR model is compared to the very detailed population model, namely, the conductance-based refractory density model. The comparison of this model with the full RD model shows the coincidence of the first peak of activity after the start of stimulation as well as the stationary state. As an example of the simulation of coupled adaptive neuronal populations, a ring model has been constructed, which reproduces a visual illusion named tilt after-effect. The FR model is recommended for the mathematical analysis of neuronal population activity as well as for computationally expensive large-scale simulations.