To better reconstruct underground targets based on ground-penetrating radar (GPR) data, this paper proposes a joint physics and data driven full-waveform inversion (PDD-FWI) scheme. This scheme combines a physics-based non-iterative approach and a data-driven deep neural network (DNN) to reconstruct target location, shape and permittivity accurately. Firstly, the normalized range migration algorithm (RMA) is introduced to extract the target contour and location information, which not only improves the robustness of the proposed scheme, but also ensures adaptability to different GPR equipment. Then, the GPR dielectric target reconstruction network (GPRDtrNet) is developed based on the improved U-net structure, including reducing network layers and adding multi-scale additive spatial attention gates and skip-connection structures. Compared with previous DNN-based reconstruction methods, GPRDtrNet has the advantages of small data requirement, high accuracy, strong generalization and noise tolerance. Finally, the simulated and real dataset containing kinds of targets is constructed to train and test GPRDtrNet. The results show that the proposed method can reconstruct underground dielectric targets accurately with high robustness and noise tolerance.