This paper has uncovered the possibility of directly poisoning event data streams by proposing Event Trojan framework, including two kinds of triggers, i.e., immutable and mutable triggers. Specifically, our two types of event triggers are based on a sequence of simulated event spikes, which can be easily incorporated into any event stream to initiate backdoor attacks. Additionally, for the mutable trigger, we design an adaptive learning mechanism to maximize its aggressiveness. To improve the stealthiness, we introduce a novel loss function that constrains the generated contents of mutable triggers, minimizing the difference between triggers and original events while maintaining effectiveness. Extensive experiments on public event datasets show the effectiveness of the proposed backdoor triggers. We hope that this paper can draw greater attention to the potential threats posed by backdoor attacks on event-based tasks.