Short-period strained-layer alpha-Sn/Ge superlattices lattice matched to Ge(001) substrates have been synthesized for the first time. The thin, tetragonally distorted alpha-Sn layers are stabilized by a modified molecular beam epitaxy technique with large modulation of substrate temperature during growth. Optimization of growth conditions is achieved via in situ Auger electron spectroscopy and low-energy electron diffraction. This new kind of strained-layer superlattice is characterized by transmission electron microscopy, x-ray diffraction, and Raman scattering. Distinct superlattice effects are observed in the structural and phonon properties of the samples.