In diffusion-based molecular communications, time synchronization is a major reason for the increase of system structure complexity. In this paper, we consider the asynchronous receiver design for molecular communications with information symbols conveyed in the time of released molecules. The main contribution of this paper is that we develop a detector called clock-free asynchronous receiver design (CFARD), in which the receiver recovers the information symbols without measuring the arrival time of molecules. The theoretical analysis indicates that compared with the synchronous receiver designs, the proposed scheme considerably lowers the structure complexity for information demodulation, which is of great significance to the feasibility of nano-scale molecular communications systems with the limitation of energy and size. The numerical results show that in the comparison of bit error ratio (BER) performance, the proposed asynchronous receiver design outperforms the synchronous linear average filter (LAF) detector and approaches to the synchronous maximum likelihood (ML) detector and first arrival (FA) detector.