In this paper, a multi-fractal algorithm for vibration signal fault diagnosis is proposed to compute the multi-fractal dimension (Dq) automatically and perform the fault diagnosis accurately. This extended G-P generalized multi-fractal dimension algorithm is based on the qth-order correlation integral and the Grassberger-Procaccia (G-P) mono fractal correlation dimension algorithm. Experiment results verify the feasibility and effectiveness of the proposed algorithm. The obtained Dq unambiguously identifies the vibration signals sampled at the various states and provides more information of the vibration signals than the mono fractal correlation dimension . Hence it should be a more effective tool for vibration signal fault diagnosis. The analysis also indicates that the fluctuation amplitude of Dq is related with the frequency component distribution of the vibration signal.