Pre-trained Natural Language Processing (NLP) models, which can be adapted to a variety of downstream language tasks via fine-tuning, highly accelerate the learning progress of NLP models. However, NLP models have been shown to be vulnerable to backdoor attacks. Previous NLP backdoor attacks mainly focus on one specific task. This limitation makes existing solutions less applicable to different NLP models which have been widely used in various tasks.In this work, we propose BadPre, the first backdoor attack against various downstream models built based on pre-trained NLP models. BadPre can launch trojan attacks against different language tasks with the same trigger.The key insight of our approach is that downstream models can inherit the security characteristics from the pre-trained models. Specifically, we leverage data posing to the pre-trained NLP models and then inference the downstream models with sentences embedded triggers. Furthermore, to fool backdoor detectors, we design a novel adversarial attack method to generate a more robust trigger.Experimental results indicate that our approach can effectively attack a wide range of downstream NLP tasks and exhibit significant robustness against backdoor detectors.