<p>The application of blockchain technology on mobile devices requires significant computing resources. However, the limited capacity of mobile devices cannot meet the high computing power requirements of blockchain technology, which limits the development and implementation of blockchain application. Mobile Edge Computing (MEC) is capable of alleviate the limited computing capacity of IoT terminals. This paper introduces a MEC-enabled blockchain system consisting of an edge computing allocation center (ECAC), multiple edge service providers (ESPs), and multiple miners. To efficiently allocate resources between these ESPs and miners, a hierarchical computation offloading strategy based on contract theory and matching game is proposed. During contract design phase, ECAC makes a contribution-reward contract to attract ESPs to join the trading market, and provide services to miners. By analyzing the attributes and conditions of feasible contract, the optimal contract is devised using Lagrange multiplication. During matching phase, an iterative matching algorithm (IMA) is proposed to achieve the matching between ESPs and miners by constructing preference sets. Both the stability and convergence of IMA have been proved by theoretical analysis. Finally, we conduct experiments to validate the feasibility and effectiveness of the design contract, and the stability of IMA has also demonstrated by experimental results.</p>