In the field of autonomous driving, online High-definition (HD) map construction is crucial for planning tasks. Recent studies have developed several high-performance HD map construction models to meet the demand. However, the point sequences generated by recent HD map construction models are jittery or jagged due to prediction bias and impact subsequent tasks. To mitigate this jitter issue, we propose the Anti-Disturbance Map construction framework (ADMap), which contains Multi-scale Perception Neck (MPN), Instance Interactive Attention (IIA), and Vector Direction Difference Loss (VDDL). By exploring the point sequence relations between and within instances in a cascading manner, our proposed ADMap effectively monitors the point sequence prediction process, and achieves state-of-the-art performance on the nuScenes and Argoverse2 datasets. Extensive results demonstrate its ability to produce stable and reliable map elements in complex and changing driving scenarios.