Current jailbreaking work on large language models (LLMs) aims to elicit unsafe outputs from given prompts. However, it only focuses on single-turn jailbreaking targeting one specific query. On the contrary, the advanced LLMs are designed to handle extremely long contexts and can thus conduct multi-turn conversations. So, we propose exploring multi-turn jailbreaking, in which the jailbroken LLMs are continuously tested on more than the first-turn conversation or a single target query. This is an even more serious threat because 1) it is common for users to continue asking relevant follow-up questions to clarify certain jailbroken details, and 2) it is also possible that the initial round of jailbreaking causes the LLMs to respond to additional irrelevant questions consistently. As the first step (First draft done at June 2024) in exploring multi-turn jailbreaking, we construct a Multi-Turn Jailbreak Benchmark (MTJ-Bench) for benchmarking this setting on a series of open- and closed-source models and provide novel insights into this new safety threat. By revealing this new vulnerability, we aim to call for community efforts to build safer LLMs and pave the way for a more in-depth understanding of jailbreaking LLMs.