We present ab initio density-functional calculations for the adsorption of Te on the Ge(001) surface. Various possible adsorption geometries for the 0.5-, 0.8-, 1-, and 2-ML (monolayer) coverages of Te have been investigated. Our results for sub-monolayer coverages confirm earlier results as well as provide some new insight into the adsorption of Te. Furthermore, our results for the 2-ML coverage of Te suggest that the bonding between the overlayer and the substrate has changed significantly. This may provide useful information on possible desorption of Te in the form of strongly bonded Te-2 units.