Common Spatial Pattern (CSP) is widely used in discriminating two classes of EEG in Brain Computer Interface applications. However, the performance of the CSP algorithm is affected by noise and artifacts, and the problem is more pronounced in small training data. To overcome these drawbacks, this paper proposes a new Spatially Sparsed CSP (SSCSP) algorithm by inducing sparsity in the spatial filters. The proposed algorithm optimizes the spatial filters to emphasize the regions that have high variances between classes, and attenuates the regions with low or irregular variances which can be due to noise or artifacts. The experimental results on 14 subjects from publicly available BCI competition datasets showed that the proposed SSCSP algorithm significantly improved the performance of the subjects with poor CSP accuracy by an average of 11%. The results also showed that the obtained sparse spatial filters are more neurophysilogically relevant.