We propose a spectral-spatial linear discriminant analysis method (LDA) for dimensionality reduction in hyper-spectral image. The proposed method uses a local scatter of the small neighborhood as a regularizer to incorporate into the objective function of the LDA. The intrinsic idea is to design an optimal linear transformation that makes these samples among the neighborhood approximate the local mean in the low-dimensional feature space while simultaneously preserving the original property of LDA. Experimental results based on both adequate training samples and inadequate training samples demonstrate that the proposed method outperforms several traditional dimensionality reduction methods.