In recent years, DNA computing has become a hotspot in the field of computing due to its unique parallel processing capabilities and nanoscale operations. DNA strand displacement (DSD) reactions, as a flexible and efficient molecular computing mechanism, provide a feasible approach for implementing complex logic and mathematical computations at the molecular level. The Tanh activation function plays a crucial role in artificial neural networks by applying nonlinear transformations to the input, enabling the network to fit complex functional relationships. As a result, the Tanh function is widely used in deep learning, signal processing, and other fields, making it an indispensable component of neural networks. In this paper, we successfully implement the Tanh function using DSD technology. Firstly, several computational modules are constructed based on the DSD circuits. Secondly, the Tanh function is realized by cascading these modules. Finally, experiments are simulated using the Visual DSD software and the results verify the reliability of the proposed approach. This work not only provides a new direction for DNA computing but also opens up new prospects for the development of bio-computing, promoting the cross-disciplinary integration of computer science and biotechnology.