Rock burst is a dynamic and complex phenomenon caused by numerous factors in underground excavating. It is very difficult to make evaluations accurately, especially under incomplete information. In this paper, a methodology for rock burst intensity evaluation is proposed based on grey target decision-making theory and variable weight synthesis thought. Some main factors that influence rock burst intensity are systematically analyzed to establish the evaluation index system. A balance function is introduced to investigate the variability of attribute weight, and then the weights of contribution factors are determined by utilizing variable weight synthesis, in conjunction with grey entropy algorithm. With respect to incomplete information in reality, the annular grey target theory is first proposed to address risk level of rock burst. Different distribution sets of bull’s eye distance are constructed to quantitatively represent corresponding intensity degree. Eventually, the application and performance comparison are carried out to demonstrate the feasibility and precision of the proposed model. It is demonstrated that the outcomes of the proposed model completely coincide with actual states. Compared with rough set theory and Russenes criterion, the proposed model can efficiently reduce decision ambiguity and produce a distinct risk measurement. It provides a new resolution for the research of rock burst evaluation under limited data.