Deploying high-performance vision transformer (ViT) models on ubiquitous Internet of Things (IoT) devices to provide high-quality vision services will revolutionize the way we live, work, and interact with the world. Due to the contradiction between the limited resources of IoT devices and resource-intensive ViT models, the use of cloud servers to assist ViT model training has become mainstream. However, due to the larger number of parameters and floating-point operations (FLOPs) of the existing ViT models, the model parameters transmitted by cloud servers are large and difficult to run on resource-constrained IoT devices. To this end, this paper proposes a transmission-friendly ViT model, TFormer, for deployment on resource-constrained IoT devices with the assistance of a cloud server. The high performance and small number of model parameters and FLOPs of TFormer are attributed to the proposed hybrid layer and the proposed partially connected feed-forward network (PCS-FFN). The hybrid layer consists of nonlearnable modules and a pointwise convolution, which can obtain multitype and multiscale features with only a few parameters and FLOPs to improve the TFormer performance. The PCS-FFN adopts group convolution to reduce the number of parameters. The key idea of this paper is to propose TFormer with few model parameters and FLOPs to facilitate applications running on resource-constrained IoT devices to benefit from the high performance of the ViT models. Experimental results on the ImageNet-1K, MS COCO, and ADE20K datasets for image classification, object detection and semantic segmentation tasks demonstrate that the proposed model outperforms other state-of-the-art models. Specifically, TFormer-S achieves 5% higher accuracy on ImageNet-1K than ResNet18 with 1.4$\times$ fewer parameters and FLOPs.