We report the first experimental demonstration of room-temperature spin transport in n-type Ge epilayers grown on a Si(001) substrate. By utilizing spin pumping under ferromagnetic resonance, which inherently endows a spin battery function for semiconductors connected with the ferromagnet, a pure spin current is generated in the n-Ge at room temperature. The pure spin current is detected by using the inverse spin Hall effect of either Pt or Pd electrode on the n-Ge. A theoretical model including a geometrical contribution allows to estimate a spin diffusion length in n-Ge at room temperature to be 660 nm. The temperature dependence of the spin relaxation time provides evidence for Elliott-Yafet spin relaxation mechanism.