In this paper, we apply kernel principal component analysis (kPCA), which has been successfully used for image denoising, to speech enhancement. In contrast to other enhancement methods which are based on the magnitude spectrum, we rather apply kPCA to complex spectral data. This is facilitated by Gaussian kernels. In the experiments, we show good noise reduction with few artifacts for noise corrupted speech at different SNR levels using additive white Gaussian noise. We compared kPCA with linear PCA and spectral subtraction and evaluated all algorithms with perceptually motivated quality measures.