Abstract: Grey theory is one of the research methods of uncertainty, which is superior in the mathematical analysis of systems with uncertain information. This study develops a data processing method with grey theory toward data fusion for ship navigation and collision avoidance system. In view of the information complementarities between Automatic Radar Plotting Aid (ARPA) radar and Automatic Identification System (AIS), we fuse AIS information with ARPA radar and present an information fusion framework based on gray theory to provide more accurate and reliable data for ship navigation and collision avoidance system. Owning to the lack of track association based on fuzzy mathematics and statistics, we propose a novel track association algorithm based on grey theory. The simulation results demonstrate that the identification accuracy is 98-99% in the circumstance of about 40 target ships. It has a high matching rate of track association.