The primary aim of a Brain-Computer Interface (BCI) is to provide communication capabilities through brain signals recorded from the scalp for those with brain disorders to be able to interact with the outside world. In order to properly decode the electroencephalographic (EEG) brain signals, the BCI needs to adapt to the subject via calibration to ensure stable performance. One of the major challenges in realization of the EEG signals is the long calibration time required since they show significant variations between recording sessions even for the same subject within the same experimental condition. This paper proposes a score-based adaptive training algorithm that maximally utilizes relevant information from prior recording sessions and significantly shortens the calibration time. Also the proposed method is suitable to develop real-time, wearable, and low-power BCI embedded devices. The BCI developed in this work is based on the P300 word speller application introduced by Farwell and Donchin in 1988. The experimental results show that by employing few letters for calibration, the proposed adaptive training algorithm can achieve 100% classification accuracy.