Molecular communication (MC) is a promising paradigm, which conveys messages at the nano- or micro- scale for information exchange by using molecules or particles as signal carriers. Clock synchronization between transmitters and receivers in MC systems plays an important role in information exchange and nanodevices' collaboration. The current research about the synchronization mainly focuses on fixed MC systems. However, the movements of transmitters and receivers commonly exist in MC systems. In this paper, two clock synchronization schemes, the least square method and the peak time method, are proposed to estimate the clock offset between a mobile transmitter and a mobile receiver in mobile MC systems. The synthesis time of information molecules is also taken into consideration in the proposed schemes, and by using different types of molecules, the influence of the synthesis time of molecules can be solved. The effects of the movement of receiver on the received signal are discussed. The performance of the proposed schemes is evaluated by simulations and discussed.