Millimeter-wave radar plays a vital role in 3D object detection for autonomous driving due to its all-weather and all-lighting-condition capabilities for perception. However, radar point clouds suffer from pronounced sparsity and unavoidable angle estimation errors. To address these limitations, incorporating a camera may partially help mitigate the shortcomings. Nevertheless, the direct fusion of radar and camera data can lead to negative or even opposite effects due to the lack of depth information in images and low-quality image features under adverse lighting conditions. Hence, in this paper, we present the radar-camera fusion network with Hybrid Generation and Synchronization (HGSFusion), designed to better fuse radar potentials and image features for 3D object detection. Specifically, we propose the Radar Hybrid Generation Module (RHGM), which fully considers the Direction-Of-Arrival (DOA) estimation errors in radar signal processing. This module generates denser radar points through different Probability Density Functions (PDFs) with the assistance of semantic information. Meanwhile, we introduce the Dual Sync Module (DSM), comprising spatial sync and modality sync, to enhance image features with radar positional information and facilitate the fusion of distinct characteristics in different modalities. Extensive experiments demonstrate the effectiveness of our approach, outperforming the state-of-the-art methods in the VoD and TJ4DRadSet datasets by $6.53\%$ and $2.03\%$ in RoI AP and BEV AP, respectively. The code is available at https://github.com/garfield-cpp/HGSFusion.