The development of fast and robust brain–computer interface (BCI) systems requires non-complex and efficient computational tools. The modern procedures adopted for this purpose are complex which limits their use in practical applications. In this study, for the first time, and to the best of our knowledge, a successive decomposition index (SDI)-based feature extraction approach is utilized for the classification of motor and mental imagery electroencephalography (EEG) tasks. First of all, the public datasets IVa, IVb, and V from BCI competition III were denoised using multiscale principal analysis (MSPCA), and then a SDI feature was calculated corresponding to each trial of the data. Finally, six benchmark machine learning and neural network classifiers were used to evaluate the performance of the proposed method. All the experiments were performed for motor and mental imagery datasets in binary and multiclass applications using a 10-fold cross-validation method. Furthermore, computerized automatic detection of motor and mental imagery using SDI (CADMMI-SDI) is developed to describe the proposed approach practically. The experimental results suggest that the highest classification accuracy of 97.46% (Dataset IVa), 99.52% (Dataset IVb), and 99.33% (Dataset V) was obtained using feedforward neural network classifier. Moreover, a series of experiments, namely, statistical analysis, channels variation, classifier parameters variation, processed and unprocessed data, and computational complexity, were performed and it was concluded that SDI is robust for noise, and a non-complex and efficient biomarker for the development of fast and accurate motor and mental imagery BCI systems.