Some characteristics of bearing initial signals are considered including unobvious features, susceptibility to noise interference and strong nonlinearity when a bearing was damaged. Based on the fractal box dimension, an improved variational mode decomposition for nonlinear features extraction of bearing fault signals（IVMD-NFE） is proposed. Because of the multi-measurement of nonlinear signals, the multifractal detrended fluctuation analysis（MF-DFA） method is used to study the multifractal characteristics of each fault signal. Taking the experimental data of rolling bearing as the research object, IVMD-NFE and MF-DFA method were used to analyze and diagnose the initial bearing signal. The results show that the signal extracted by the IVMD-NFE method can filter out noise to a greater extent and has lower fractal box dimension, and the extracted nonlinear characteristics are more representative; The fault signals of bearing exhibit multi-fractal features, the outer ring fault has the largest singularity index and strongest nonlinearity, and the cage fault is the smallest and weakest nonlinearity, indicating that the complexity of the data can better reflect the running state of the bearing. However, the method of using VMD or directly processing the original signal fails to extract effective nonlinear features, resulting in failure to distinguish faults.