A new method called Local and Global Preserving Embedding (LGPE) is proposed for manifold learning. This method assumes a global embedding function in low dimensional space, then incorporates the relative compactness information of the data distributions on the global geometry to reconstruct sample data. Finally, the global low dimensional submanifold is obtained by minimizing the cost function.The LGPE preserves the local and global structures of the data points simultaneously, and can obtain better dimensionality reduction on the sparse Swiss-roll dataset with noises (N=400, SNR=10 dB) and COIL-20 multi-poses dataset.When it is used in the AT&T face dateset,the recognition rate can be improved by 15% as compared with that of other local manifold methods under condition of embedding dimension lower than 40. The experimental results on both synthetic and real data sets show that proposed method is effectiveness and robustness for noise and sparse data.