Diffusive molecular communication (DMC), in which molecules are used to deliver information in diffusion channel, is one of the most prominent systems in nanonetworks. In particular, the research on end-to-end mobile DMC system is even more challenging. In this paper, we investigate the energy efficiency of multi-hop mobile DMC system. First, the energy model for this system is proposed based on the mobilities of transmitter nanomachine (TN), relays and receiver nanomachine (RN). Then the mathematical expressions of total energy consumption and throughput are derived. Furthermore, the energy efficiency which is defined as the throughput per unit energy consumption is analyzed. Finally, the numerical results show that the parameters including the diffusion coefficients and velocities of mobile TN, relays and RN, the initial distance of each hop, the number of molecules emitted in each time slot by TN and relays, and each time slot duration have different impacts on the energy efficiency. How to set these system parameters can be used to provide guidelines for designing energy efficient multi-hop mobile DMC system.