Cerenkov Luminescence Tomography (CLT) is a novel and potential imaging modality which can display the three-dimensional distribution of radioactive probes. However, due to severe ill-posed inverse problem, obtaining accurate reconstruction results is still a challenge for traditional model-based methods. The recently emerged deep learning-based methods can directly learn the mapping relation between the surface photon intensity and the distribution of the radioactive source, which effectively improves the performance of CLT reconstruction. However, the previously proposed deep learning-based methods cannot work well when the order of input is disarranged. In this paper, a novel 3D graph convolution-based residual network, GCR-Net, is proposed, which can obtain a robust and accurate reconstruction result from the photon intensity of the surface. Additionally, it is proved that the network is insensitive to the order of input. The performance of this method was evaluated with numerical simulations and in vivo experiments. The results demonstrated that compared with the existing methods, the proposed method can achieve efficient and accurate reconstruction in localization and shape recovery by utilizing three-dimensional information.Cerenkov Luminescence Tomography (CLT) is a novel and potential imaging modality which can display the three-dimensional distribution of radioactive probes. However, due to severe ill-posed inverse problem, obtaining accurate reconstruction results is still a challenge for traditional model-based methods. The recently emerged deep learning-based methods can directly learn the mapping relation between the surface photon intensity and the distribution of the radioactive source, which effectively improves the performance of CLT reconstruction. However, the previously proposed deep learning-based methods cannot work well when the order of input is disarranged. In this paper, a novel 3D graph convolution-based residual network, GCR-Net, is proposed, which can obtain a robust and accurate reconstruction result from the photon intensity of the surface. Additionally, it is proved that the network is insensitive to the order of input. The performance of this method was evaluated with numerical simulations and in vivo experiments. The results demonstrated that compared with the existing methods, the proposed method can achieve efficient and accurate reconstruction in localization and shape recovery by utilizing three-dimensional information.