A method has been developed to reconstruct the tracks of γ-rays that have undergone Compton scattering in a high-resolution detector system. The development of this method is focussed on applications in nuclear γ-ray spectroscopy. In nuclear in-beam γ-ray spectroscopy a number of (position-sensitive) germanium detectors are placed around a target where the nuclei under investigation are produced. The γ-rays emitted by the nuclei can have energies up to several MeVs. The nuclear reactions in the target can cause emission of up to 25 coincident γ-rays and sometimes even more. In order to resolve the individual γ-rays from such events the detector systems currently under development will have such a high granularity that the energy of scattered γ-rays will be deposited in several different detector segments. Therefore, in order to determine the initial energies and the first interaction positions, the tracks have to be reconstructed. The reconstruction method presented in this paper is based on the observation that the energy deposition of the final photoelectric interaction after scattering usually falls in a narrow energy band. Starting from points in this energy range attempts are made to reconstruct the tracks using the photoelectric and Compton interaction probabilities and the Compton scattering formula. The method has been tested on simulated events with up to 25 coincident γ-rays of various energies and with different detector position resolutions. Reconstruction efficiencies of up to 84% have been achieved.