In this work, we introduce a phenomenological model describing the thermoelectric power of icosahedral quasicrystals. On the basis of a realistic model for the spectral conductivity, obtained from ab initio band-structure calculations ͓C. Landauro and H. Solbrig, Physica B 301, 267 ͑2000͔͒, we derive a closed analytical expression for the Seebeck coefficient, satisfactorily describing its temperature dependence S(T) over a wide temperature range. We introduce four phenomenological coefficients relating the electronic structure to characteristic features of the experimental S(T) curves. By comparing our analytical results with available experimental data we relate the sensitivity of the thermopower curve to minor variations in the chemical composition to a systematic shift of the Fermi-level position.