With the great advancements in large language models (LLMs), adversarial attacks against LLMs have recently attracted increasing attention. We found that pre-existing adversarial attack methodologies exhibit limited transferability and are notably inefficient, particularly when applied to LLMs. In this paper, we analyze the core mechanisms of previous predominant adversarial attack methods, revealing that 1) the distributions of importance score differ markedly among victim models, restricting the transferability; 2) the sequential attack processes induces substantial time overheads. Based on the above two insights, we introduce a new scheme, named TF-Attack, for Transferable and Fast adversarial attacks on LLMs. TF-Attack employs an external LLM as a third-party overseer rather than the victim model to identify critical units within sentences. Moreover, TF-Attack introduces the concept of Importance Level, which allows for parallel substitutions of attacks. We conduct extensive experiments on 6 widely adopted benchmarks, evaluating the proposed method through both automatic and human metrics. Results show that our method consistently surpasses previous methods in transferability and delivers significant speed improvements, up to 20 times faster than earlier attack strategies.