A new nonlinear principle component analysis (PCA) method, hidden space principal component analysis (HSPCA) is presented in this paper. Firstly, the data in the input space is mapped into a high hidden space by a nonlinear function whose role is similar to that of hidden neurons in Artificial Neural Networks. Then the goal of features extraction and data compression will be implemented by performing PCA on the mapped data in the hidden space. Compared with linear PCA method, our algorithm is a nonlinear PCA one essentially and can extract the data features more efficiently. While compared with kernel PCA method presented recently, the mapped samples are exactly known and the conditions satisfied by nonlinear mapping functions are more relaxed. The unique condition is symmetry for kernel function in HSPCA. Finally, experimental results on artificial and real-world data show the feasibility and validity of HSPCA.