In order to predict the rock burst disasters of coal roadway, the coal with bump tendency is regarded as a perfectly elastic-brittle material, and the mechanical model of circular coal roadway is established to analyze the distribution characteristics of stress and deformation energy density of surrounding rock of coal roadway, and then the rock burst prediction model of coal roadway is established to predict the rock burst disaster of coal roadway. The results show that the tangential stress and deformation energy density of the surrounding rock of elastic-brittle coal roadway jump at the interface between the elastic zone and the failure zone. The damage degree of the strength and in-situ stress of coal increase, and the radius of failure area also increases. As a result, the jump height of the tangential stress and deformation energy density of the surrounding rock of the coal roadway increases. The tangential stress jumping provides a force for the instability and failure of coal roadway, and the deformation energy density jumping provides an energy for the rock burst. The higher the tangential stress and deformation energy density jump, the easier the instability and rock burst of coal become. Based on the jumping of tangential stress and deformation energy density, the analytical prediction model of rock burst in coal roadway is established, and the prediction results are consistent with the actual situation of rock burst in the field, thus providing a new method for predicting rock burst in brittle coal roadway.