SummaryMobile edge computing (MEC) promotes the development and popularity of Internet of Things (IoT) devices with higher connectivity and ultra‐low latency through network topology optimization and real‐time data analysis. With the exponential growth of data traffic generated by IoT devices, it is essential to prevent edge servers (ESs) from overloading through efficient task scheduling to ensure the quality of service (QoS). However, the lack of trust and incentive mechanisms between ESs deployed and managed by different infrastructure providers makes it challenging to perform peer‐offloaded tasks. Moreover, to meet the low‐latency requirement of many IoT applications, the execution efficiency of the task scheduling scheme in MEC needs to be improved. To address the above challenges systematically, a QoS‐driven task scheduling scheme with blockchain in MEC named SharpEdge is proposed. In SharpEdge, ESs publish tasks with rewards and then select the most reliable executors through a historical performance‐based reputation mechanism to perform peer offloading. The performance of the executor will be recorded into the blockchain after the task is completed. In addition, a concurrent consensus mechanism using sharding technology is designed, improving task scheduling efficiency. We implement SharpEdge based on Hyperledger Fabric and verify its performance in a simulated MEC environment.