Temporal knowledge graph (TKG) reasoning aims to predict the future missing facts based on historical information and has gained increasing research interest recently. Lots of works have been made to model the historical structural and temporal characteristics for the reasoning task. Most existing works model the graph structure mainly depending on entity representation. However, the magnitude of TKG entities in real-world scenarios is considerable, and an increasing number of new entities will arise as time goes on. Therefore, we propose a novel architecture modeling with relation feature of TKG, namely aDAptivE path-MemOry Network (DaeMon), which adaptively models the temporal path information between query subject and each object candidate across history time. It models the historical information without depending on entity representation. Specifcally, DaeMon uses path memory to record the temporal path information derived from path aggregation unit across timeline considering the memory passing strategy between adjacent timestamps. Extensive experiments conducted on four real-world TKG datasets demonstrate that our proposed model obtains substantial performance improvement and outperforms the state-of-the-art up to 4.8% absolute in MRR.