Video-based person re-identification (Re-ID) is a prominent computer vision topic due to its wide range of video surveillance applications. Most existing methods utilize spatial and temporal correlations in frame sequences to obtain discriminative person features. However, inevitable degradations, e.g., motion blur contained in frames often cause ambiguity texture noise and temporal disturbance, leading to the loss of identity-discriminating cues. Recently, a new bio-inspired sensor called event camera, which can asynchronously record intensity changes, brings new vitality to the Re-ID task. With the microsecond resolution and low latency, event cameras can accurately capture the movements of pedestrians even in the aforementioned degraded environments. Inspired by the properties of event cameras, in this work, we propose a Sparse-Dense Complementary Learning Framework, which effectively extracts identity features by fully exploiting the complementary information of dense frames and sparse events. Specifically, for frames, we build a CNN-based module to aggregate the dense features of pedestrian appearance step-by-step, while for event streams, we design a bio-inspired spiking neural backbone, which encodes event signals into sparse feature maps in a spiking form, to present the dynamic motion cues of pedestrians. Finally, a cross feature alignment module is constructed to complementarily fuse motion information from events and appearance cues from frames to enhance identity representation learning. Experiments on several benchmarks show that by employing events and SNN into Re-ID, our method significantly outperforms competitive methods.