Pre-trained models (PTMs) have been widely used in various downstream tasks. The parameters of PTMs are distributed on the Internet and may suffer backdoor attacks. In this work, we demonstrate the universal vulnerability of PTMs, where fine-tuned PTMs can be easily controlled by backdoor attacks in arbitrary downstream tasks. Specifically, attackers can add a simple pre-training task, which restricts the output representations of trigger instances to pre-defined vectors, namely neuron-level backdoor attack (NeuBA). If the backdoor functionality is not eliminated during fine-tuning, the triggers can make the fine-tuned model predict fixed labels by pre-defined vectors. In the experiments of both natural language processing (NLP) and computer vision (CV), we show that NeuBA absolutely controls the predictions for trigger instances without any knowledge of downstream tasks. Finally, we apply several defense methods to NeuBA and find that model pruning is a promising direction to resist NeuBA by excluding backdoored neurons. Our findings sound a red alarm for the wide use of PTMs.