Large Language Models (LLMs) power numerous AI applications, yet updating their knowledge remains costly. Model editing provides a lightweight alternative through targeted parameter modifications, with meta-learning-based model editing (MLME) demonstrating strong effectiveness and efficiency. However, we find that MLME struggles in low-data regimes and incurs high training costs due to the use of KL divergence. To address these issues, we propose $\textbf{E}$fficient $\textbf{M}$ulti-$\textbf{S}$tep $\textbf{Edit (EMSEdit)}$, which leverages multi-step backpropagation (MSBP) to effectively capture gradient-activation mapping patterns within editing samples, performs multi-step edits per sample to enhance editing performance under limited data, and introduces norm-based regularization to preserve unedited knowledge while improving training efficiency. Experiments on two datasets and three LLMs show that EMSEdit consistently outperforms state-of-the-art methods in both sequential and batch editing. Moreover, MSBP can be seamlessly integrated into existing approaches to yield additional performance gains. Further experiments on a multi-hop reasoning editing task demonstrate EMSEdit's robustness in handling complex edits, while ablation studies validate the contribution of each design component. Our code is available at https://github.com/xpq-tech/emsedit.