A multi-modal knowledge graph (MKG) includes triplets that consist of entities and relations and multi-modal auxiliary data. In recent years, multi-hop multi-modal knowledge graph reasoning (MMKGR) based on reinforcement learning (RL) has received extensive attention because it addresses the intrinsic incompleteness of MKG in an interpretable manner. However, its performance is limited by empirically designed rewards and sparse relations. In addition, this method has been designed for the transductive setting where test entities have been seen during training, and it works poorly in the inductive setting where test entities do not appear in the training set. To overcome these issues, we propose TMR (Topology-aware Multi-hop Reasoning), which can conduct MKG reasoning under inductive and transductive settings. Specifically, TMR mainly consists of two components. (1) The topology-aware inductive representation captures information from the directed relations of unseen entities, and aggregates query-related topology features in an attentive manner to generate the fine-grained entity-independent features. (2) After completing multi-modal feature fusion, the relation-augmented adaptive RL conducts multi-hop reasoning by eliminating manual rewards and dynamically adding actions. Finally, we construct new MKG datasets with different scales for inductive reasoning evaluation. Experimental results demonstrate that TMP outperforms state-of-the-art MKGR methods under both inductive and transductive settings.