As the main cause of failure and damage to rotating machinery, rolling bearing failure can result in huge economic losses. As the rolling bearing vibration signal is nonlinear and has non-stationary characteristics, the health status information distributed in the rolling bearing vibration signal is complex. Using common time-domain or frequency-domain approaches cannot easily enable an accurate assessment of rolling bearing health. In this paper, a novel rolling bearing fault diagnostic method based on multi-dimensional characteristics was developed to meet the requirements for accurate diagnosis of different fault types and severities with real-time computational performance. First, a multi-dimensional feature extraction algorithm based on entropy characteristics, Holder coefficient characteristics and improved generalized fractal box-counting dimension characteristics was performed to extract the health status feature vectors from the bearing vibration signals. Second, a grey relation algorithm was employed to achieve bearing fault pattern recognition intelligently using the extracted multi-dimensional feature vector. This experimental study has illustrated that the proposed method can effectively recognize different fault types and severities after integration of the improved fractal box-counting dimension into the multi-dimensional characteristics, in comparison with existing pattern recognition methods.