Mobile edge computing (MEC) can reduce the latency of cloud computing successfully. However, the edge server may fail due to the hardware of software issues. When the edge server failure happens, the users who offload tasks to this server will be affected. How to recover the services for these affected users quickly and effectively is challenging. Moreover, considering that the server failure is continuous and temporary, and the failed server can be repaired, the previous works cannot handle this problem effectively. Therefore, in this paper, we propose the fast, online, distributed, and temporary failure recovery algorithm (FODT) for MEC. In FODT, when edge sever failure happens, only the affected APs recalculate their user-server allocation strategies and the other APs do not change their strategies. For the affected access points (Aps), the strategies before server failure are reused to reduce complexity and latency. When the failed server is repaired, the influenced APs reuse the strategies before server failure to offload task to this server. Based on this approach, the FODT can achieve better performance than previous works. To the best of knowledge, the FODT is the first failure recovery algorithm, and when compared with previous research, it has higher failure recovery efficiency and lower complexity with acceptable approximate ratio.