We present a novel 3D pose estimation method based on joint interdependency (JI) for acquiring 3D joints from the human pose of an RGB image. The JI incorporates the body part based structural connectivity of joints to learn the high spatial correlation of human posture on our method. Towards this goal, we propose a new long short-term memory (LSTM)-based deep learning architecture named propagating LSTM networks (p-LSTMs), where each LSTM is connected sequentially to reconstruct 3D depth from the centroid to edge joints through learning the intrinsic JI. In the first LSTM, the seed joints of 3D pose are created and reconstructed into the whole-body joints through the connected LSTMs. Utilizing the p-LSTMs, we achieve the higher accuracy of about 11.2% than state-of-the-art methods on the largest publicly available database. Importantly, we demonstrate that the JI drastically reduces the structural errors at body edges, thereby leads to a significant improvement.