Graph neural architecture search (GraphNAS) has shown great potential for automatically designing graph neural architectures for graph related tasks. However, multi-task GraphNAS capable of handling multiple tasks simultaneously has been largely unexplored in literature, posing great challenges to capture the complex relations and influences among different tasks. To tackle this problem, we propose a novel multi-task graph neural architecture search with task-aware collaboration and curriculum (MTGC3), which is able to simultaneously discover optimal architectures for different tasks and learn the collaborative relationships among different tasks in a joint manner. Specifically, we design the layer-wise disentangled supernet capable of managing multiple architectures in a unified framework, which combines with our proposed soft task-collaborative module to learn the transferability relationships between tasks. We further develop the task-wise curriculum training strategy to improve the architecture search procedure via reweighing the influence of different tasks based on task difficulties. Extensive experiments show that our proposed MTGC3 model achieves state-of-the-art performance against several baselines in multi-task scenarios, demonstrating its ability to discover effective architectures and capture the collaborative relationships for multiple tasks.