We are developing a Compton telescope based on high resolution Si and CdTe detectors for astrophysical observations in sub-MeV/MeV gamma-ray region. Recently, we constructed a prototype Compton telescope which consists of six layers of double-sided Si strip detectors and CdTe pixel detectors to demonstrate the basic performance of this new technology. By irradiating the detector with gamma-rays from radio isotope sources, we have succeeded in Compton reconstruction of images and spectra. The obtained angular resolution is 3.9 • (FWHM) at 511 keV, and the energy resolution is 14 keV (FWHM) at the same energy. In addition to the conventional Compton reconstruction, i.e., drawing cones in the sky, we also demonstrated a full reconstruction by tracking Compton recoil electrons using the signals detected in successive Si layers. By irradiating 137 Cs source, we successfully obtained an image and a spectrum of 662 keV line emission with this method. As a next step, development of larger double-sided Si strip detectors with a size of 4 cm × 4 cm is underway to improve the effective area of the Compton telescope. We are also developing a new low-noise analog ASIC to handle the increasing number of channels. Initial results from these two new technologies are presented in this paper as well.