The surface electronic structure of Gd(0001)/W(110) has been studied by scanning tunneling spectroscopy in dependence of the coverage. An exchange split dz2-like surface state which is well known from photoemission experiments was already found for coverages as low as 2 ML. The exchange splitting was found to increase with increasing coverage up to the fourth ML. For higher coverages the electronic structure remains constant. We found spectra that are shifted by ≈ 25 meV, possibly due to stacking faults.