<p>Pursuit evasion is a game with intricate patterns. In this domain, the pursuer tries to catch the evader by reducing the distance. Similarly, the evader aims to avoid capture and to reach the target. We have to face considerable computational complexity and environmental uncertainty in this situation. To solve this problem, the existing research studies utilise many practical techniques. Still, due to their complex pattern analysis, these techniques fail to address major issues like real-time decision-making, long-term planning, handling uncertainty and multi-agent coordination. This study aims to provide an effective solution by involving neural networks to improve pursuit-evasion game tactics. The proposed research presents a novel technique combining the advanced neural networks called Hybrid Neural Strategy Network (HNSN). These proposed techniques combine Deep Neural Network (DNN) and Artificial Neural Network (ANN). By using these combined strengths, HNSN aims to address the major problem discussed earlier. To avoid capture and barriers effectively, the evader's technique uses these combined techniques for long-term trajectory predictions and immediate path modifications. At the same time, the pursuers prepare the best-captured pathways by predicting the evader's movements using the HNSN. ANN makes real-time reactions possible, and behavioral analysis by DNN is used to refine the strategy. Simulation tests have proved the effectiveness of the HNSN in different scenarios. The outcomes show the efficacy of HNSN to improve pursuit-evasion game tactics by showing notable improvement in MAE score, success rate, and successful positions of both pursuer and evader. This novel integration of ANN and DNN techniques under HNSN provides an effective solution to the challenges of pursuit-evasion games and provides an important contribution to the domain.</p>