Motor imagery-based brain–computer interfaces (MI-BCIs) have great application prospects in motor enhancement and rehabilitation. However, the capacity to control a MI-BCI varies among persons. Predicting the MI ability of a user remains challenging in BCI studies. We first calculated the relative power level (RPL), power spectral entropy (PSE) and Lempel–Ziv complexity (LZC) of the resting-state open and closed-eye EEG of different frequency bands and investigated their correlations with the upper and lower limbs MI performance (left hand, right hand, both hands and feet MI tasks) on as many as 105 subjects. Then, the most significant related features were used to construct a classifier to separate the high MI performance group from the low MI performance group. The results showed that the features of open-eye resting alpha-band EEG had the strongest significant correlations with MI performance. The PSE performed the best among all features for the screening of the MI performance, with the classification accuracy of 85.24%. These findings demonstrated that the alpha bands might offer information related to the user’s MI ability, which could be used to explore more effective and general neural markers to screen subjects and design individual MI training strategies.