In the graph-based dimensionality reduction methods, which have been successfully applied in many practical problems such as face recognition, graph construction plays a key role. However, the commonly used graph construction approaches, which are based on the Euclidean distance, usually suffer the problem of the unfit description of the distances between images. The image Euclidean distance (IMED), which uses the prior knowledge that pixels located near one another have little variance in gray scale values and defines a metric matrix according to the spatial distance between pixels, has been proved more reasonable than Euclidean distance for images. So, in this paper, an image Euclidean distance based graph (IEG), which utilizes IMED as the distance metric, is proposed and the corresponding dimensionality reduction method called image Euclidean graph preserving projections (IEGPP) is also derived. As a result, the IEG can effectively fit the intrinsic distance of images. IEGPP naturally inherits the characteristics of IEG and maintains the attractive properties of graph preserving. The feasibility and effectiveness of the proposed method are verified on three popular face databases (ORL, Yale and FERET) with promising results.