In recent years, Vision Transformer (ViT) has prevailed among computer vision tasks for its powerful capability of image representation. Frustratingly, the manual design of efficient architectures for ViTs can be time-consuming, often requiring repetitive trial and error. Moreover, existing lightweight ViTs have not been thoroughly explored, leading to weaker performance compared to convolutional neural networks. To address these challenges, we propose Adaptive Search for Broad attention based Vision Transformers, called ASB, which incorporates broad attention and adaptive neural architecture evolution to strengthen light-weight ViTs. The inclusion of broad attention within the search space allows us to explore novel architectures that can significantly enhance the performance of light-weight ViTs by providing more comprehensive attention information. We also design an efficient adaptive evolutionary algorithm to explore effective architectures by dynamically adjusting the probability distribution of candidate mutation operators. Our experimental results show that the adaptive evolution in ASB can efficiently learn excellent light-weight models, achieving a 55% improvement in convergence speed over traditional evolutionary algorithms. Moreover, the effectiveness of ASB is demonstrated in several visual tasks, including image classification, mobile COCO panoptic segmentation, and mobile ADE20K semantic segmentation. For instance, on ImageNet, searched model achieves 77.8% performance with 6.5M parameters, resulting in a 0.7% accuracy improvement over the state-of-the-art EfficientNet-B0. On mobile COCO panoptic segmentation, our approach outperforms prevalent MobileNetV2 by 7.4% PQ. On mobile ADE20K semantic segmentation, our method attains 40.9% mIoU, which exceeds MobileNetV2 with 6.9% mIoU.