Brain-Computer Interfaces (BCI) will revolutionize the way people with severe impairment of speech production can communicate. While current efforts focus on training classifiers on vast amounts of neurophysiological signals to decode imagined speech, much less attention has been given to users' ability to adapt their neural activity to improve BCI-control. To address whether BCI-control improves with training and characterize the underlying neural dynamics, we trained 15 healthy participants to operate a binary BCI system based on electroencephalography (EEG) signals through syllable imagery for five consecutive days. Despite considerable interindividual variability in performance and learning, a significant improvement in BCI-control was globally observed. Using a control experiment, we show that a continuous feedback about the decoded activity is necessary for learning to occur. Performance improvement was associated with a broad EEG power increase in frontal theta activity and focal enhancement in temporal low-gamma activity, showing that learning to operate an imagined-speech BCI involves dynamic changes in neural features at different spectral scales. These findings demonstrate that combining machine and human learning is a successful strategy to enhance BCI controllability.