Recently, facial priors based face super-resolution (SR) methods have obtained significant performance gains in dealing with extremely degraded facial images, and facial priors have also been proved useful in facilitating the inference of face images. Based on this, how to fully fuse facial priors into deep features to improve face SR performance has attracted a major attention. In this paper, we propose a learning-based face SR approach with incremental boosting facial parsing information (IFPSR) for high-magnification of low-resolution faces. The proposed IFPSR method consists of three main parts: i) a three-stage parsing map embedded features upsampling network, in which image recovery and prior estimation processes are performed simultaneously and progressively to improve the image resolution; ii) a progressive training method and a joint facial attention and heatmap loss to obtain better facial attributes; iii) the channel attention strategy in residual dense blocks to adaptively learn facial features. Extensive experimental results show that compared with the state-of-the-art methods in terms of quantitative and qualitative metrics, our approach can achieve an outstanding balance between SR image quality and low network complexity.