We have proposed a new approach to pattern recognition in which not only a classifier but also a feature space of input variables is learned incrementally. In this paper, an extended version of Incremental Principal Component Analysis (IPCA) and Resource Allocating Network with Long-Term Memory (RAN-LTM) are effectively combined to implement this idea. Since IPCA updates a feature space incrementally by rotating the eigen-axes and increasing the dimensions, the inputs of a neural classifier must also change in their values and the number of input variables. To solve this problem, we derive an approximation of the update formula for memory items, which correspond to representative training samples stored in the long-term memory of RAN-LTM. With these memory items, RAN-LTM is efficiently reconstructed and retrained to adapt to the evolution of the feature space. This function is incorporated into our face recognition system. In the experiments, the proposed incremental learning model is evaluated over a self-compiled video clip of 24 persons. The experimental results show that the incremental learning of a feature space is very effective to enhance the generalization performance of a neural classifier in a realistic face recognition task.