Quality assessment of natural images is influenced by perceptual mechanisms, e.g., attention and contrast sensitivity, and quality perception can be generated in a hierarchical process. This paper proposes an architecture of Attention Integrated Hierarchical Image Quality networks (AIHIQnet) for no-reference quality assessment. AIHIQnet consists of three components: general backbone network, perceptually guided neck network, and head network. Multi-scale features extracted from the backbone network are fused to simulate image quality perception in a hierarchical manner. The attention and contrast sensitivity mechanisms modelled by an attention module capture essential information for quality perception. Considering that image rescaling potentially affects perceived quality, appropriate pooling methods in the non-convolution layers in AIHIQnet are employed to accept images with arbitrary resolutions. Comprehensive experiments on publicly available databases demonstrate outstanding performance of AIHIQnet compared to state-of-the-art models. Ablation experiments were performed to investigate the variants of the proposed architecture and reveal importance of individual components.