Based on the definition of intrinsic scale component (ISC), a new self-adaptive time-frequency analysis method,i.e., local characteristic-scale decomposition (LCD), was proposed. By using LCD, a complicated signal can be decomposed into a number of ISC,whose instantaneous frequencies have physical meaning.The processed simulation signal was analyzed by LCD and empirical mode decomposition (EMD). The analysis results have demonstrated the validity of the two decomposition methods. Moreover, LCD is superior to EMD in computational efficiency and restriction of end effects. In addition, LCD is also applied to fault diagnosis for roller bearing and the analysis results from the actual fault vibration signal have further proved the effectiveness of LCD.