The theory and experiment of quantum information have been studied extensively in recent years, and the feasibility of quantum communication has been proved. Although the fundamental technology is not yet mature, research on quantum internet should be conducted. To implement quantum internet, an architecture that describes how quantum nodes are linked to form networks and how protocol functions are vertically composed need to be developed urgently. In this paper, we present a novel design of a cluster-based structure to describe how quantum nodes are interconnected, and how the structure can improve the performance of qubit transmission and reduce the network complexity. The idea of the quantum local area network (QLAN) is proposed as an essential component of the quantum internet. Besides, each quantum repeater links to neighboring repeaters to form a core network, and multiple QLANs are connected through the core network. The core network can be grouped into different hierarchical quantum repeater networks according to needed service requirements. For the sake of interoperability and fast prototyping, we adopt the idea of OSI layering model of the current Internet in the design of quantum internet. Finally, we elaborate on the composition of quantum nodes and the realization of end-to-end communication.