Vision-Language Pre-training (VLP) models have exhibited unprecedented capability in many applications by taking full advantage of the learned multimodal alignment. However, previous studies have shown they are vulnerable to maliciously crafted adversarial samples. Despite recent success, these attacks are generally instance-specific and require generating perturbations for each input sample. In this paper, we reveal that VLP models are also susceptible to the instance-agnostic universal adversarial perturbation (UAP). Specifically, we design a novel Contrastive-training Perturbation Generator with Cross-modal conditions (C-PGC). In light that the pivotal multimodal alignment in VLP models is achieved via contrastive learning, we devise to turn this powerful weapon against VLP models themselves. I.e., we employ a malicious version of contrastive learning to train the proposed generator using our carefully crafted positive and negative image-text pairs. Once training is complete, the generator is able to produce universal perturbations that can essentially destroy the established alignment relationship in VLP models. Besides, C-PGC fully utilizes the characteristics of Vision-and-Language (V+L) scenarios by incorporating both unimodal and cross-modal information as effective guidance. Extensive experiments show that C-PGC successfully forces adversarial samples to move away from their original area in the VLP model's feature space, thus fundamentally enhancing attack performance across various victim models and V+L tasks.