In this manuscript, a novel dual-step selective epitaxy growth (SEG) of Ge was proposed to significantly decrease the defect density and to create fully strained relaxed Ge on a Si substrate. With the single-step SEG of Ge, the threading defect density (TDD) was successfully decreased from 2.9 × 107 cm−2 in a globally grown Ge layer to 3.2 × 105 cm−2 for a single-step SEG and to 2.84 × 105 cm−2 for the dual-step SEG of the Ge layer. This means that by introducing a single SEG step, the defect density could be reduced by two orders of magnitude, but this reduction could be further decreased by only 11.3% by introducing the second SEG step. The final root mean square (RMS) of the surface roughness was 0.64 nm. The strain has also been modulated along the cross-section of the sample. Tensile strain appears in the first global Ge layer, compressive strain in the single-step Ge layer and fully strain relaxation in the dual-step Ge layer. The material characterization was locally performed at different points by high resolution transmission electron microscopy, while it was globally performed by high resolution X-ray diffraction and photoluminescence.