In the present study, a Compton camera simulator based on the GEANT4 detector simulation tool kit and MATLABTM, and designated the Compton Imaging Simulator (CIS), was developed. The software system encompasses a simulator, an image-reconstruction algorithm, and a data analysis tool. The computational time to obtain a sufficient number of Compton scattered data was dramatically reduced using the source-biasing and exponential transform techniques. Also, a four-dimensional Monte Carlo simulation capability was incorporated. A comparison of the simulation results with the experimental results shows that the CIS accurately simulates the Compton camera.