Most existing embodied manipulation methods predominantly rely on end-to-end learning strategies. Although performing adequately on specific tasks, these approaches often treat physical interaction as a black box, thereby sacrificing interpretability and suffering from insufficient geometric grounding, large error accumulation in long-horizon planning, and weak adaptability to complex dynamics. To address fine-grained manipulation in unstructured scenarios, this article proposes an embodied manipulation framework based on a 3D geometric world model （3D-GWM） and conditional flow matching, termed 3D-GWM, which comprises three modules: 3D perception and compression, a generative geometric world model, and conditional flow-matching-based action generation. In the perception module, a complementary dual-domain feature enhancement algorithm is proposed to jointly capture spatial high-frequency details and global frequency-domain context, together with an instruction-driven dynamic token compression mechanism to reduce computation while preserving feature fidelity. In deployment evaluations, the number of input visual tokens is reduced from 2 048 to 128, while the peak GPU memory usage is reduced from 58.7 GB to 17.2 GB. In the cognition module, an intermediate-frame prediction strategy is adopted. By predicting stage-wise 3D geometric terminal states of sub-tasks, it provides intermediate goal guidance with causal logic for long-horizon manipulation and mitigates error accumulation during planning. In the execution module, a conditional flow matching strategy is employed. By using geometric anchors to construct target vector fields, it generates smooth trajectories that satisfy physical contact constraints and reduces the risk of singularities commonly encountered in rigid inverse-kinematics solvers. Experimental results show that 3D-GWM achieves an average success rate of 89.4% in simulation and 82.0% on the real robot for complex-logic and high-precision tasks; compared with representative baseline methods, the average success rate increases by 7.0% and 8.75%, respectively.