Large amounts of incremental learning algorithms have been proposed to alleviate the catastrophic forgetting issue arises while dealing with sequential data on a time series. However, the adversarial robustness of incremental learners has not been widely verified, leaving potential security risks. Specifically, for poisoning-based backdoor attacks, we argue that the nature of streaming data in IL provides great convenience to the adversary by creating the possibility of distributed and cross-task attacks -- an adversary can affect \textbf{any unknown} previous or subsequent task by data poisoning \textbf{at any time or time series} with extremely small amount of backdoor samples injected (e.g., $0.1\%$ based on our observations). To attract the attention of the research community, in this paper, we empirically reveal the high vulnerability of 11 typical incremental learners against poisoning-based backdoor attack on 3 learning scenarios, especially the cross-task generalization effect of backdoor knowledge, while the poison ratios range from $5\%$ to as low as $0.1\%$. Finally, the defense mechanism based on activation clustering is found to be effective in detecting our trigger pattern to mitigate potential security risks.