The Local characteristic-scale decomposition（ LCD） method is improved in this paper. The reason of appearance of the stagnation point on low frequency intrinsic scale component（ ISC） is analyzed and a new method which called eliminate stagnation point-based Local characteristic-scale decomposition method is presented. The results from the simulation signal have shown the obvious advantages of the improved LCD method. Based on the improvement of the LCD,the combination of the LCD and envelope analysis is applied to the roller bearing fault diagnosis. The roller bearing vibration signals is composed by the improved LCD into some intrinsic scale component（ ISC）. The envelope analysis method based on Hilbert is used to analyze the ISCs and the work state of rolling bearing can be identified. The experimental results showed that the improved LCD method and Envelopment analysis method have a good result to apply to the rolling bearing fault diagnosis.