The battery-free sensor network is an emerging IoT network architecture. The battery-free sensor network aims to address the energy and lifetime limitations in traditional wireless sensor networks. In the battery-free sensor network, battery-free nodes can harvest energy from the ambient environment by specific energy harvesting component. Since the energy in the ambient environment is infinite, the lifetime of the battery-free sensor networks is unlimited in terms of energy. Thus, the lifetime limitation of the wireless sensor network can be addressed. However, since the ambient energy is usually very weak and it distributes unevenly, the coverage problem in battery-free sensor networks is very complex than that in traditional wireless sensory networks. In order to solve the coverage problem in battery-free sensor networks and more reasonably use the harvested energy, a battery-free sensor network is considered in which battery-free nodes have multi-level communication radius. Furthermore, a coverage problem is defined in such networks. It is proved that this problem is NP-Hard, and an approximation algorithm is proposed to solve this problem. The approximation ratio of such algorithm is analyzed and the simulations are also carried out to evaluate the performance of the algorithm. The results demonstrate that the algorithm is effective and efficient.