A kernel-based independent component analysis algorithm, which combines Kernel principal component analysis (KPCA) and Independent component analysis (ICA) is proposed for anomaly detection in hyperspectral imagery. Firstly, KPCA is performed on a feature space associated with the original hyperspectral data space via a certain nonlinear mapping function to whiten data and fully mine the nonlinear information between spectral bands. Then, ICA seeks the projection directions in the KPCA whitened space for making the distribution of the projected data mutually independent. Finally, RX detector is performed on the projected data to locate the anomaly targets. The kernel ICA algorithm saved the nonlinear information on dimension reduction in hyperspectral data and made the extracted features mutually independent, so improved the performance of RX detector in hyperspectral data. Numerical experiments are conducted on real hyperspectral images. Using receiver operating characteristic curves, the results show the improved performance and reduction in the false-alarm rate.