In this paper, we introduce a new method of data transformation for finger vein recognition system. Our proposed method uses kernel mapping functions to map the data before performing Principal Component Analysis. Kernel Principal Component Analysis (KPCA) is a well-known extension of PCA which is suitable for finding nonlinear patterns as it maps the data nonlinearly. In this work we develop an extension of KPCA which is both faster and more appropriate than KPCA for finger vein recognition system. The proposed method is called Feature Dependent Kernel Principal Component Analysis (FDKPCA). In FDKPCA the data is mapped differently from KPCA resulting in lower-dimension feature space where more important and valuable features are selected and extracted. Furthermore, extensive experiments reveal the significance of the proposed method for finger vein recognition systems.