Despite the fact that Recommender Systems have been researched and developed for quite a while, they still hold some certain challenges, two of which are Cold Start and Data Sparsity. Being introduced as a savior, the Cross-domain Recommender system (CDR) owns the capacity to transfer knowledge across domains which makes it become the practical solution for the mentioned issues. In CDR approaches, the family of graph-based solutions is very effective, which builds graphs to illustrate the relationship between users, items, and other factors and learn their representations through graph representation learning. However, most graph-based approaches focus on extracting either domain-specific or domain-shared features and do not have the mechanism to prevent the transfer of private features, which can degrade the quality of vector representations. Moreover, the knowledge transfer process built on overlapping users makes the model biased toward these users, thus downgrading the performance on cold-start users. This paper proposes a meta-GRS framework that uses Graph Neural Network with Meta-Learning and Adversarial Learning for cross-domain recommendation. In meta-GRS, the representative user and item embeddings are improved thanks to the features extracted by the private and cross-domain graphs. Domain-shared features are learned under adversarial learning such that the domain discriminator is unable to determine whether the domain they came from can ensure the positive transfer. To optimize the model performance effectively, we use a Dynamic Weight Averaging algorithm to learn loss weights automatically. The model's parameters are optimized under the optimization-based meta-learning method provides our model the capability of generalization to the new users. Experiments on practical datasets illustrate that the meta-GRS leads the chart in the comparison of other state-of-the-art baselines in recommendation accuracy.