Estimating accurate 3D human poses from 2D images remains a challenge due to the lack of explicit depth information in 2D data. This paper proposes an improved mixture density network for 3D human pose estimation called the Locally Connected Mixture Density Network (LCMDN). Instead of conducting direct coordinate regression or providing unimodal estimates per joint, our approach predicts multiple possible hypotheses by the Mixture Density Network (MDN). Our network can be divided into two steps: the 2D joint points are estimated from the input images first; then, the information of human joints correlation is extracted by a feature extractor. After the human pose feature is extracted, multiple pose hypotheses are generated via the hypotheses generator. In addition, to make better use of the relationship between human joints, we introduce the Locally Connected Network (LCN) as a generic formulation to replace the traditional Fully Connected Network (FCN), which is applied to a feature extraction module. Finally, to select the most appropriate 3D pose result, a 3D pose selector based on the ordinal ranking of joints is adopted to score the predicted pose. The LCMDN improves the representation capability and robustness of the original MDN method notably. Experiments are conducted on the Human3.6M and MPII dataset. The average Mean Per Joint Position Error (MPJPE) of our proposed LCMDN reaches 50 mm on the Human3.6M dataset, which is on par or better than the state-of-the-art works. The qualitative results on the MPII dataset show that our network has a strong generalization ability.