Dragonflies visually detect prey and conspecifics, rapidly pursuing these targets via acrobatic flights. Over many decades, studies have investigated the elaborate neuronal circuits proposed to underlie this rapid behaviour. A subset of dragonfly visual neurons exhibit exquisite tuning to small, moving targets even when presented in cluttered backgrounds. In prior work, these neuronal responses were quantified by computing the rate of spikes fired during an analysis window of interest. However, neuronal systems can utilize a variety of neuronal coding principles to signal information, so a spike train's information content is not necessarily encapsulated by spike rate alone. One example of this is burst coding, where neurons fire rapid bursts of spikes, followed by a period of inactivity. Here we show that the most studied target-detecting neuron in dragonflies, CSTMD1, responds to moving targets with a series of spike bursts. This spiking activity differs from those in other identified visual neurons in the dragonfly, indicative of different physiological mechanisms underlying CSTMD1's spike generation. Burst codes present several advantages and disadvantages compared to other coding approaches. We propose functional implications of CSTMD1's burst coding activity and show that spike bursts enhance the robustness of target-evoked responses.