How to extract forecast feature and distinguish degeneration status is the key problem in fault forecasting and it will influence its veracity. Fractal dimension could describe its complexity and irregularity in quantity. Fractal dimension based on mathematical morphology is a kind of calculation method based on mathematical cover. The definition of mathematical cover was expanded first in the paper and three kinds of generalized estimation method for mathematical morphological fractal dimension were proposed. The accuracy and efficiency were contrasted and analyzed by means of emulation. On this basis, applying mathematical fractal dimension into forecast feature extracting for bearing fault. Its relevance and stability were analyzed and proved. In the last, combining mathematical morphology, fractal geometry and grey theory, a kind of bearing degradation status identification based on mathematical morphological fractal dimension and grey relational analysis was proposed, The effectiveness of this process was verified via processing of experiment data.