Image aesthetic assessment (IAA) is a highly significant research topic in computational aesthetics, with a wide range of applications in areas such as art creation. However, existing IAA methods ignore the influence of multilevel aesthetic attributes as well as compositional features on the evaluation results. In this paper, we propose an IAA model MFCI-Net that integrates multilevel deep features and composition cognition. The model combines both local and global aesthetic features of an image using ResNet50 and Swin Transformer architectures to receive image information from different receptive fields, enhancing the ability to understand the complex image content. Furthermore, MFCI-Net employs the holistically nested edge detection (HED) algorithm to guide the network to learn the association between spatial structure and aesthetic features, improving its performance on the IAA tasks. Extensive experiments were conducted on three public datasets, namely AADB, PARA, and KonIQ-10K, to evaluate the performance of MFCI-Net. The results demonstrate the superiority of our model in obtaining both multi-level deep features and spatial composition features of an image. Our code will be released at https://github.com/liuxida/MFCI-Net .