IV-VI diluted magnetic semiconductor Ge1-xCrxTe layers up to x=0.1 were grown on SrF2 substrates by molecular beam epitaxy. In site reflection high-energy electron diffraction shows a streaky pattern with sixfold symmetry in the plane for the Ge1-xCrxTe layer, implying an epitaxial growth of Ge1-xCrxTe [111]/SrF2 [111]. A clear hysteresis loop is observed in the anomalous Hall effect measurements due to the strong spin-orbit interaction in the host GeTe. The Curie temperature increases with increasing Cr composition up to 200 K, but there is no clear dependence of the Curie temperature on the hole concentration, implying that the mechanism of the ferromagnetic interaction among Cr ions is different from Mn doped diluted magnetic semiconductors.