Accelerating the development of the 5G network and Internet of Things (IoT) application, multi-access edge computing (MEC) in a small-cell network (SCN) is designed to provide computation-intensive and latency-sensitive applications through task offloading. However, without collaboration, the resources of a single MEC server are wasted or sometimes overloaded for different service requests and applications; therefore, it increases the user’s task failure rate and task duration. Meanwhile, the distinct MEC server has faced some challenges to determine where the offloaded task will be processed because the system can hardly predict the demand of end-users in advance. As a result, the quality-of-service (QoS) will be deteriorated because of service interruptions, long execution, and waiting time. To improve the QoS, we propose a novel Fuzzy logic-based collaborative task offloading (FCTO) scheme in MEC-enabled densely deployed small-cell networks. In FCTO, the delay sensitivity of the QoS is considered as the Fuzzy input parameter to make a decision where to offload the task is beneficial. The key is to share computation resources with each other and among MEC servers by using fuzzy-logic approach to select a target MEC server for task offloading. As a result, it can accommodate more computation workload in the MEC system and reduce reliance on the remote cloud. The simulation result of the proposed scheme show that our proposed system provides the best performances in all scenarios with different criteria compared with other baseline algorithms in terms of the average task failure rate, task completion time, and server utilization.