Federated learning (FL) has emerged as a promising strategy for collaboratively training complicated machine learning models from different medical centers without the need of data sharing. However, the traditional FL relies on a central server to orchestrate the global model training among clients. This makes it vulnerable to the failure of the model server. Meanwhile, the model trained based on the global data property may not yield the best performance on the local data of a particular site due to the variations of data characteristics among them. To address these limitations, we proposed Gossip Mutual Learning(GML), a decentralized collaborative learning framework that employs Gossip Protocol for direct peer-to-peer communication and encourages each site to optimize its local model by leveraging useful information from peers through mutual learning. On the task of tumor segmentation on PET/CT images using HECKTOR21 dataset with 223 cases from five clinical sites, we demonstrated GML could improve tumor segmentation performance in terms of Dice Similarity Coefficient (DSC) by 3.2%, 4.6% and 10.4% on site-specific testing cases as compared to three baseline methods: pooled training, FedAvg and individual training, respectively. We also showed GML has comparable generalization performance as pooled training and FedAvg when applying them on 78 cases from two out-of-sample sites where no case was used for model training. In our experimental setup, GML showcased a sixfold decrease in communication overhead compared to FedAvg, requiring only 16.67% of the total communication overhead.