Safety-critical cyber physical systems usually require controllers that not only meet performance goal but also guarantee safety. However, the existing neural controller synthesis methods require a large number of data samples and gradient steps, which makes the real-time training infeasible when system dynamics vary over time. To address the challenge, we propose HyML-ASCS, a hybrid meta-learning framework for adaptive safety controller synthesis. HyML-ASCS combines model-based meta-learning, to generate task-specific embeddings that capture the patterns of safety controller synthesis tasks, with gradient-based meta-learning, to efficiently adapt to new synthesis tasks. This approach speeds up convergence, reduces the number of iterations required, and improves synthesis success rates, making HyML-ASCS a scalable and efficient solution for real-time control synthesis in dynamic environments. We evaluate HyML-ASCS on several benchmarks, demonstrating that it outperforms existing state-of-the-art methods in terms of synthesis efficiency, success rate, and scalability.