Objective: Navigation through tortuous and deformable vessels using catheters with limited steering capability underscores the need for reliable path planning. State-of-the-art path planners do not fully account for the deformable nature of the environment. Methods: This work proposes a robust path planner via a learning from demonstrations method, named Curriculum Generative Adversarial Imitation Learning (C-GAIL). This path planning framework takes into account the interaction between steerable catheters and vessel walls and the deformable property of vessels. Results: In-silico comparative experiments show that the proposed network achieves a 38% higher success rate in static environments and 17% higher in dynamic environments compared to a state-of-the-art approach based on GAIL. In-vitro validation experiments indicate that the path generated by the proposed C-GAIL path planner achieves a targeting error of 1.26±0.55mm and a tracking error of 5.18±3.48mm. These results represent improvements of 41% and 40% over the conventional centerline-following technique for targeting error and tracking error, respectively. Conclusion: The proposed C-GAIL path planner outperforms the state-of-the-art GAIL approach. The in-vitro validation experiments demonstrate that the path generated by the proposed C-GAIL path planner aligns better with the actual steering capability of the pneumatic artificial muscle-driven catheter utilized in this study. Therefore, the proposed approach can provide enhanced support to the user in navigating the catheter towards the target with greater accuracy, effectively meeting clinical accuracy requirements. Significance: The proposed path planning framework exhibits superior performance in managing uncertainty associated with vessel deformation, thereby resulting in lower tracking errors.