A stable and robust odometry system is essential for autonomous robot navigation. The 4D millimeter-wave radar, known for its resilience in harsh weather conditions, has attracted considerable attention. As the latest generation of FMCW radar, 4D millimeter-wave radar provides point clouds with both position and Doppler velocity information. However, the increased uncertainty and noise in 4D radar point clouds pose challenges that prevent the direct application of LiDAR-based SLAM algorithms. To address this, we propose a SLAM framework that fuses 4D radar data with gyroscope readings using graph optimization techniques. Initially, Doppler velocity is employed to estimate the radar’s ego velocity, with dynamic points being removed accordingly. Building on this, we introduce a pre-integration factor that combines ego-velocity and gyroscope data. Additionally, leveraging the stable RCS characteristics of radar, we design a corresponding point selection method based on normal direction and propose a scan-to-submap point cloud registration technique weighted by RCS intensity. Finally, we validate the reliability and localization accuracy of our framework using both our own dataset and the NTU dataset. Experimental results show that the proposed DGRO system outperforms traditional 4D radar odometry methods, especially in environments with slow speeds and fewer dynamic objects.