Various adaptation techniques have been proposed to address the non-stationarity issue faced by electroencephalogram (EEG)-based brain-computer interfaces (BCIs). However, most of these adaptation techniques are only suitable for binary-class BCIs. This paper proposes a supervised multiclass data space adaptation technique (MDSA) to transform the test data using a linear transformation such that the distribution difference between the multiclass train and test data is minimized. The results of using the proposed MDSA on BCI Competition IV dataset 2a improved the classification accuracy by an average of 4.3% when 20 trials per class were used from the test session to estimate adaptation transformation. The results also showed that the proposed MDSA algorithm outperformed the multi pooled mean linear discrimination (MPMLDA) technique with as few as 10 trials per class used for calculating the transformation matrix. Hence the results showed the effectiveness of the proposed MDSA algorithm in addressing non-stationarity issue for multiclass EEG-based BCI.