A new image reconstruction method was developed for a Compton camera. A simulation to determine a γ-ray source position was performed by using the simulation tool, GEANT4. An image reconstruction was made in two steps. First, a three dimensional image was constructed and projected in one selected plane, then the points from each ellipse was picked up by taking the peak points of a density distribution of crossing points between the ellipse and the first step image. The second step procedure improved the accuracy and the spatial resolution of a position determination significantly, comparing with the image obtained by only the first step. The accuracy and the resolution for a point source were obtained to be about 0.02 mm and (1.35±0.15) mm, respectively. The same procedure was applied to an imaging of the distributed γ-ray source.