In recent years, biological neural networks have developed rapidly due to their advantages of fast parallel computing processing speed and strong fault tolerance. This article is dedicated to explore innovation in this field and successfully constructing a Hopfield neural network model based on DNA strand displacement (DSD) circuits. First, this article constructs four core functional modules based on DSD, including an encoder module, weighted sum module, comparator module, and decoder module. These functional modules together form the design foundation of the DSD circuit, achieving effective circuit construction. Second, the construction of the Hopfield neural network is achieved through DSD circuits. The construction of this network achieves the integration of DSD technology and neural networks. Finally, the Sudoku conjecture problem is solved through the neural network. This article conducts a simulation in visual DSD, which verifies the feasibility of Sudoku conjecture. Our work integrates DSD technology with neural networks and uses them to solve practical problems. This fusion broadens the research field of neural networks and demonstrates the potential of biotechnology in practical applications.