With the rapid development of new media formats, various high-definition display devices are ubiquitous, and high-resolution (HR) images are essential for high-quality visual experiences. Quality assessment of HR images has become an urgent challenge. However, conventional image quality assessment (IQA) methods with good performance are designed for low-resolution (LR) images, which lacks the perceptual characteristics of HR images, resulting in difficult to achieve satisfactory subjective consistency. Moreover, huge computational costs would have to be consumed when applying those deep neural networks in LR-IQA directly to HR images. Inspired by the fact that regions with rich textures are more sensitive to distortion than others, texture dominated no-reference image quality assessment for HR images are proposed in this paper. Specifically, a dual branch network based on multi-scale technology was designed to extract texture and semantic features separately, and cross scale and dual dimensional attention were introduced to ensure the dominance of texture features. Then, multi-layer perception network is used to map the extracted quality perception feature vectors to the predicted quality score. Worthy of note is that local entropy has been calculated and representative blocks are cropped as inputs to the feature extraction network, greatly reducing computational complexity. Overall, the texture dominated high-resolution IQA network (TD-HRNet) proposed utilizes a reference free method, while could perform excellently on HR datasets of different sizes, image types, and distortion types, accurately predicting the quality of different types of HR images.