Parametric edge curve extraction from 3D point clouds is a challenging task in computer vision due to the diverse, complex, sparse, and noisy characteristics of the data. In this paper, we propose a novel edge curve extraction network, named DRC-Net, which leverages Density Reweighted Convolution to address the challenge of incomplete edge curve structure encountered in prior research. Inspired by PIE-Net, we employ density-reweighted convolution instead of the conventional feature extraction module and deconvolution to supplant the feature propagation module, thereby preserving both translation and displacement invariance. Our DRC-Net is architected to simultaneously execute feature point classification and edge curve extraction, utilizing a standard encoder-decoder network structure. We evaluate the performance of DRC-Net on the ABC dataset, the largest publicly available dataset of CAD models, through robustness testing and comparison with EC-Net and PIE-Net. Experimental results demonstrate that the proposed method can effectively improve the accuracy in feature points classification and edge extraction while producing relatively complete and smooth edge curves.