Collision avoidance between unmanned aerial vehicles (UAVs) and non-cooperative targets (e.g., off-nominal operations or birds) presents significant challenges in urban air mobility (UAM). This difficulty arises due to the highly dynamic and unpredictable flight intentions of these targets. Traditional collision-avoidance methods primarily focus on cooperative targets or non-cooperative ones with fixed behavior, rendering them ineffective when dealing with highly unpredictable flight patterns. To address this, we introduce a deep reinforcement learning-based collision-avoidance approach leveraging global and local intent prediction. Specifically, we propose a Global and Local Perception Prediction Module (GLPPM) that combines a state-space-based global intent association mechanism with a local feature extraction module, enabling accurate prediction of short- and long-term flight intents. Additionally, we propose a Fusion Sector Flight Control Module (FSFCM) that is trained with a Dueling Double Deep Q-Network (D3QN). The module integrates both predicted future and current intents into the state space and employs a specifically designed reward function, thereby ensuring safe UAV operations. Experimental results demonstrate that the proposed method significantly improves mission success rates in high-density environments, with up to 80 non-cooperative targets per square kilometer. In 1000 flight tests, the mission success rate is 15.2 percentage points higher than that of the baseline D3QN. Furthermore, the approach retains an 88.1% success rate even under extreme target densities of 120 targets per square kilometer. Finally, interpretability analysis via Deep SHAP further verifies the decision-making rationality of the algorithm.