The existing three-dimensional (3D) human hand pose estimation algorithms do not fully exploit the characteristics of fingers and the key features. To solve this problem, a finger-point reinforcement (FPR) strategy and a multi-layer fusion squeeze and excitation (MFSE) block are proposed. The FPR strategy highlights the role of the finger position points in the human hand point cloud, strengthens the attention of network feature extraction layers to the finger position points in the point cloud, and improves the regression accuracy of the finger joint points. The MFSE block improves the ability of the layered network to extract and express local features. This module realizes the fusion and weight distribution of different levels of features between the layered networks, thereby enhancing the robustness of the model and the accuracy of human hand pose estimation. Experiments on two public benchmark datasets, MSRA and ICVL, verify that the proposed algorithm can achieve high-precision 3D human hand pose estimation.