Non-invasive brain-computer interface (BCI) can be used in imagined speech recognition to aid people with speech disorders and has been investigated in different languages. However, this technology is in a very early stage for Bengali speech recognition. Therefore, the aim of this research is to develop a BCI system that can recognize imagined Bengali speech. In this study, a non-invasive 14-channel electroencephalography (EEG) headset was employed to record the EEG signals from 30 subjects. The subjects were instructed to imagine 11 Bengali vowels ▪ and 10 digits ▪. Then, we extracted four statistical features from the recorded EEG signals. A coarse-to-fine level classification was performed to categorize the imagined EEG data by exploiting these features. The data was classified at coarse level to distinguish between a vowel and a digit. Each vowel and digit were then classified at the fine level. In our classification, random forest achieved the highest recognition accuracy of 84.28% at the coarse level and 76.13% at the fine level. In order to comprehend the role played by each brain lobe in recognizing imagined speech, we additionally examined each of the brain lobes. The frontal lobe demonstrated the highest accuracy, with a coarse level accuracy of 80.65% and a fine level accuracy of 66.31%. Moreover, the proposed model outperformed the reported literature in this field.