Our ability to understand and control the emergence of order in swarming systems is a fundamental challenge in contemporary science. The standard Vicsek model (SVM) — a minimal model for swarming systems of self-propelled particles — describes a large population of agents reaching global alignment without the need of central control. Yet, the emergence of order in this model takes time and is not robust to noise. In many real-world scenarios, we need a decentralized protocol to guide a swarming system (e.g., unmanned vehicles or nanorobots) to reach an ordered state in a prompt and noise-robust manner. Here, we find that introducing a simple adaptive rule based on the heading differences of neighboring particles in the Vicsek model can effectively speed up their global alignment, mitigate the disturbance of noise to alignment, and maintain a robust alignment under predation. This simple adaptive model of swarming systems could offer new insights in understanding the prompt and flexible formation of animals and help us design better protocols to achieve fast and robust alignment for multi-agent systems.