Hyperspectral imagery contains a wealth of spectral and spatial information that can improve target detection and recognition performance. Conventional feature extraction methods cannot fully exploit both spectral and spatial information. Data fusion by simply stacking different feature sources together does not take into account the differences between feature sources. In this paper, a local graph-based fusion (LGF) method is proposed to couple dimension reduction and feature fusion of the spectral information (i.e., the spectra in the HS image) and the spatial information [extracted by morphological profiles (MPs)]. In the proposed method, the fusion graph is built on the full data by moving a sliding window from the first pixel to the last one. This yields a clear improvement over a previous approach with fusion graph built on randomly selected samples. Experimental results on real hyperspectral images are very encouraging. Compared to the methods using only single feature and stacking all the features together, the proposed LGF method improves the overall classification accuracy on one of the data sets for more than 20% and 5%, respectively.