In pose estimation methods based on keypoint voting schemes, the accuracy of estimated pose depends on the quality of predicted candidate keypoints. However, due to sensor noise, occlusions and cluttered backgrounds, candidate keypoint prediction often involves aleatoric uncertainty. Existing methods typically do not explicitly account for the impact of uncertainty, which limits their performance in complex scenes. In this work, we propose LCKPose, a framework that quantifies the prediction uncertainty via Laplacian Candidate Keypoint modeling for Pose estimation. LCKPose employs a dual-stream hierarchical fusion network to capture fine-grained features and represents the coordinates of each candidate keypoint as a Laplace distribution. Distribution modeling enables the network to consider the uncertainty and focus on learning from reliable candidates. Moreover, on the basis of Laplace distribution modeling, LCKPose introduces a distance-based density search algorithm to locate the final predicted keypoints more effectively. Experimental results show the effectiveness of our method in reducing the adverse impact of uncertainty, achieving state-of-the-art results on the Linemod-Occlusion (89.0%) and YCB-Video (95.3%) datasets.