The airport gate assignment problem, a critical aspect of airport operations management, involves assigning incoming aircraft to available gates while meeting operational constraints. These decisions directly impact both operational efficiency and passenger satisfaction. Due to the dynamic and uncertain nature of the aviation system, frequent flight delays make pre-assignment planning challenging. To ensure efficient operations and passenger satisfaction, an advanced algorithm capable of rapidly responding to changing flight information is urgently needed. This study presents a Deep Reinforcement Learning (DRL) algorithm to address the airport gate allocation problem. Using a Markov Decision Process (MDP) framework, the trained DRL agent effectively allocates gates and quickly adapts to environmental changes. The reward function is designed to optimize both passenger walking distance and minimize apron usage, with global rewards reflecting the total walking distance and apron usage, and single-step rewards encouraging gate allocations that reduce passenger travel distances. Experimental results on benchmark scenarios show that the proposed algorithm outperforms existing methods, achieving faster solution times while maintaining competitive allocation quality.