Visual reprogramming (VR) is a prompting technique that aims to re-purpose a pre-trained model (e.g., a classifier on ImageNet) to target tasks (e.g., medical data prediction) by learning a small-scale pattern added into input images instead of tuning considerable parameters within the model. The location of the pattern within input samples is usually determined by a pre-defined mask shared across all samples. In this paper, we show that the shared mask potentially limits VR's generalization and increases its approximation error due to the lack of sample-level adaptation. Motivated by this finding, we design a new framework for VR called sample-specific multi-channel masks (SMM). Specifically, SMM employs a lightweight ConvNet and patch-wise interpolation to generate sample-specific three-channel masks instead of a shared and pre-defined mask. Since we generate different masks for individual samples, SMM is theoretically shown to reduce approximation error for the target tasks compared with existing state-of-the-art VR methods. We also empirically demonstrate its performance gain on both ResNet and ViT. The success of SMM further highlights the broader applicability of VR in leveraging the latent knowledge of pre-trained models for various target tasks. Our code is available at https://github.com/tmlr-group/SMM.