Albeit the recent progress in single image 3D human pose estimation due to the convolutional neural network, it is still challenging to handle real scenarios such as highly occluded scenes. In this paper, we propose to address the problem of single image 3D human pose estimation with occluded measurements by exploiting the Euclidean distance matrix (EDM). Specifically, we present two approaches based on EDM, which could effectively handle occluded joints in 2D images. The first approach is based on 2D-to-2D distance matrix regression achieved by a simple CNN architecture. The second approach is based on sparse coding along with a learned over-complete dictionary. Experiments on the Human3.6M dataset show the excellent performance of these two approaches in recovering occluded observations and demonstrate the improvements in accuracy for 3D human pose estimation with occluded joints.