Large Language Models (LLMs) have achieved remarkable success across diverse tasks, yet they remain vulnerable to adversarial attacks, notably the well-documented \textit{jailbreak} attack. Recently, the Greedy Coordinate Gradient (GCG) attack has demonstrated efficacy in exploiting this vulnerability by optimizing adversarial prompts through a combination of gradient heuristics and greedy search. However, the efficiency of this attack has become a bottleneck in the attacking process. To mitigate this limitation, in this paper we rethink the generation of adversarial prompts through an optimization lens, aiming to stabilize the optimization process and harness more heuristic insights from previous iterations. Specifically, we introduce the \textbf{M}omentum \textbf{A}ccelerated G\textbf{C}G (\textbf{MAC}) attack, which incorporates a momentum term into the gradient heuristic. Experimental results showcase the notable enhancement achieved by MAP in gradient-based attacks on aligned language models. Our code is available at https://github.com/weizeming/momentum-attack-llm.