Knowledge editing is a promising method for updating Large Language Models efficiently. However, previous studies often suffer from poor specificity in continual editing, as they typically focus on single edits or preventing knowledge forgetting. To address this, we propose TamEdit, a trajectory-aware meta-learning method that preserves specificity for continual knowledge editing. TamEdit unifies three levels: Inner Optimization performs multi-step fast fine-tuning on the single edit; Trajectory-based Editing unifies continual edits with a growing memory; and Outer Optimization leverages meta-learning to distill cross-task strategies for preserving specificity. By capturing the relationships between different single edits within the trajectory, our method learns how to effectively avoid specificity drift. Experiments across multiple LLMs show TamEdit significantly outperforms baselines in continual editing, improving specificity by 14.81% with fast speed (requiring only 8.84% of the time cost of most baselines), while preserving general capabilities.