The Soft Gamma-ray Detector (SGD) on board ASTRO-H (Japanese next high-energy astrophysics mission) is a Compton telescope with narrow field-of-view, which utilizes Compton kinematics to enhance its background rejection capabilities. It is realized as a hybrid semiconductor detector system which consists of silicon and CdTe (cadmium telluride) detectors. It can detect photons in a wide energy band (50-600 keV) at a background level 10 times better than that of the Suzaku Hard X-ray Detector, and is complimentary to the Hard X-ray Imager on board ASTRO-H with an energy coverage of 5-80 keV. Excellent energy resolution is the key feature of the SGD, allowing it to achieve good background rejection capability taking advantage of good angular resolution. An additional capability of the SGD, its ability to measure gamma-ray polarization, opens up a new window to study properties of gamma-ray emission processes. Here we describe the instrument design of the SGD, its expected performance, and its development status.