Choosing an appropriate kernel is one of the key problems in kernel-based methods. Most existing kernel selection methods require that the class labels of the training examples are known. In this paper, we propose an adaptive kernel selection method for kernel principal component analysis, which can effectively learn the kernels when the class labels of the training examples are not available. By iteratively optimizing a novel criterion, the proposed method can achieve nonlinear feature extraction and unsupervised kernel learning simultaneously. Moreover, a non-iterative approximate algorithm is developed. The effectiveness of the proposed algorithms are validated on UCI datasets and the COIL-20 object recognition database.