Multi-source data, either from different sensors or disparate features extracted from the same sensor, are valuable for geospatial image analysis due to their potential for providing complementary features. In this paper, a composite-kernel-based feature extraction method is proposed for multi-source remote sensing data classification. Features from different sources are first fused via a weighted composite kernel mapping, and then projected to a lower-dimensional subspace in which kernel local Fisher discriminant analysis (KLFDA) is used to extract the most discriminative information. We hypothesize that after such a projection, multi-source data would have better class separability between classes, and an efficient linear classification modelmultinomial logistic regression (MLR) would be suitable for classification. The efficacy of the proposed method is demonstrated via experiments using two different sets of multi-source geospatial data. For feature fusion, the raw spectral data and extended multi-attribute profiles (EMAPs) derived from the hyperspectral image are used as a testbed for multi-source image analysis. The second multi-source testbed used for validation involves sensor fusion, in which the hyperspectral and light detection and ranging (LiDAR) data are utilized. Experimental results show that composite kernel local Fisher's discriminant analysis when combined with MLR based classifier (CKLFDA-MLR) is very effective at feature extraction and classification of multi-source geospatial images.