Small moving objects at far distance always occupy only one or a few pixels in image and exhibit extremely limited visual features, which bring great challenges to motion detection. Highly evolved visual systems endow flying insects with remarkable ability to pursue tiny mates and prey, providing a good template to develop image processing method for small target motion detection. The insects' excellent sensitivity to small moving objects is believed to come from a class of specific neurons called small target motion detectors (STMDs). However, existing STMD-based methods often experience performance degradation when coping with complex natural scenes. In this paper, we propose a bio-inspired visual system with spatio-temporal feedback mechanism (called Spatio-Temporal Feedback STMD) to suppress false positive background movement while enhancing system responses to small targets. Specifically, the proposed visual system is composed of two complementary subnetworks and a feedback loop. The first subnetwork is designed to extract spatial and temporal movement patterns of cluttered background by neuronal ensemble coding. The second subnetwork is developed to capture small target motion information where its output and signal from the first subnetwork are integrated together via the feedback loop to filter out background false positives in a recurrent manner. Experimental results demonstrate that the proposed spatio-temporal feedback visual system is more competitive than existing methods in discriminating small moving targets from complex natural environments.