Network architectures and learning principles are key in forming complex functions in artificial neural networks (ANNs) and spiking neural networks (SNNs). SNNs are considered the new-generation artificial networks by incorporating more biological features than ANNs, including dynamic spiking neurons, functionally specified architectures, and efficient learning paradigms. In this paper, we propose a Motif-topology and Reward-learning improved SNN (MR-SNN) for efficient multi-sensory integration. MR-SNN contains 13 types of 3-node Motif topologies which are first extracted from independent single-sensory learning paradigms and then integrated for multi-sensory classification. The experimental results showed higher accuracy and stronger robustness of the proposed MR-SNN than other conventional SNNs without using Motifs. Furthermore, the proposed reward learning paradigm was biologically plausible and can better explain the cognitive McGurk effect caused by incongruent visual and auditory sensory signals.