Retrosynthetic analysis is a canonical technique for planning the synthesis route of organic molecules in drug discovery and development. In this technique, the screening of synthetic tree branches requires accurate forward reaction prediction, but existing software is far from completing this step independently. Previous studies attempted to apply a neural network to forward reaction prediction, but the accuracy was not satisfying. Through using the Edit Vector-based description and extended-connectivity fingerprints to transform the reaction into a vector, this study focuses on the update of the neural network to improve the template-based forward reaction prediction. Hard-threshold activation and the target propagation algorithm are implemented by introducing mixed convex-combinatorial optimization. Comparative tests were conducted to explore the optimal hyperparameter set. Using 15,000 experimental reaction data extracted from granted United States patents, the proposed hard-threshold neural network was systematically trained and tested. The results demonstrated that a higher prediction accuracy was obtained than that for the traditional neural network with backpropagation algorithm. Some successfully predicted reaction examples are also briefly illustrated.