Pre-trained vision models (PVMs) have become a dominant component due to their exceptional performance when fine-tuned for downstream tasks. However, the presence of backdoors within PVMs poses significant threats. Unfortunately, existing studies primarily focus on backdooring PVMs for the classification task, neglecting potential inherited backdoors in downstream tasks such as detection and segmentation. In this paper, we propose the Pre-trained Trojan attack, which embeds backdoors into a PVM, enabling attacks across various downstream vision tasks. We highlight the challenges posed by cross-task activation and shortcut connections in successful backdoor attacks. To achieve effective trigger activation in diverse tasks, we stylize the backdoor trigger patterns with class-specific textures, enhancing the recognition of task-irrelevant low-level features associated with the target class in the trigger pattern. Moreover, we address the issue of shortcut connections by introducing a context-free learning pipeline for poison training. In this approach, triggers without contextual backgrounds are directly utilized as training data, diverging from the conventional use of clean images. Consequently, we establish a direct shortcut from the trigger to the target class, mitigating the shortcut connection issue. We conducted extensive experiments to thoroughly validate the effectiveness of our attacks on downstream detection and segmentation tasks. Additionally, we showcase the potential of our approach in more practical scenarios, including large vision models and 3D object detection in autonomous driving. This paper aims to raise awareness of the potential threats associated with applying PVMs in practical scenarios. Our codes will be available upon paper publication.