We have carried out an experiment of semiconductor detector (Germanium, Ge detector) using γ rays emitting source ¹³⁷Cs at nuclear astrophysics laboratory of Okayama University in Japan. Now a days, Ge detectors are very important tools for γ ray's studies and nuclear spectroscopy research. We have measured the photo-peak efficiencies using the radioactive source ¹³⁷Cs. We have created the Monte Carlo simulation with the help of GEometry ANd and Tracking (Geant4) successfully. The photo-peak efficiencies of MC simulation were calculated. We have compared our simulation data with the experimental data. We have found fair agreement between MC data and experimental data and it within 77%.