Traffic prediction under various conditions is an important but challenging task. Latest studies have achieved promising results but suffer degraded performance without exception under abnormal conditions (e.g., accidents), as the traffic patterns under abnormal conditions often deviate from the normal seriously. To adapt to both normal and abnormal conditions, we propose the Multi-task Multi-range Multi-subgraph Attention Network (M3AN), a novel deep learning model to explicitly model the impacts of abnormal events for condition-aware traffic prediction. It constructs different subgraphs to model node features to address the abrupt traffic patterns with sparse abnormal event data, and uses an attention mechanism to capture dynamic spatial dependencies. Meanwhile, a multi-task fusion module is built upon a road-segment graph and an intersection graph to enhance the ability of capturing complicated dependencies, together with a multi-range attention module for automatically learning the influences of abnormal events with lower computational complexity. Experimental results on two real-world traffic datasets show that our M3AN outperforms state-of-the-art approaches under both normal and abnormal conditions.