Large-scale pre-trained models have achieved remarkable success in various computer vision tasks. A standard approach to leverage these models is to fine-tune all model parameters for downstream tasks, which poses challenges in terms of computational and storage costs. Recently, inspired by Natural Language Processing (NLP), parameter-efficient transfer learning has been successfully applied to vision tasks. However, most existing techniques primarily focus on single-task adaptation, and despite limited research on multi-task adaptation, these methods often exhibit suboptimal training/inference efficiency. In this paper, we first propose an once-for-all Vision Multi-Task Adapter (VMT-Adapter), which strikes approximately O(1) training and inference efficiency w.r.t task number. Concretely, VMT-Adapter shares the knowledge from multiple tasks to enhance cross-task interaction while preserves task-specific knowledge via independent knowledge extraction modules. Notably, since task-specific modules require few parameters, VMT-Adapter can handle an arbitrary number of tasks with a negligible increase of trainable parameters. We also propose VMT-Adapter-Lite, which further reduces the trainable parameters by learning shared parameters between down- and up-projections. Extensive experiments on four dense scene understanding tasks demonstrate the superiority of VMT-Adapter(-Lite), achieving a 3.96% (1.34%) relative improvement compared to single-task full fine-tuning, while utilizing merely ~1% (0.36%) trainable parameters of the pre-trained model.