The super-resolution of a very low-resolution face image is a challenge task in single image super-resolution. Most of deep learning methods learn a non-linear mapping of input-to-target space by one-step upsampling. These methods are difficult to reconstruct a high-resolution face image from single very low-resolution face image. In this paper, we propose an asymptotic Residual Back-Projection Network (RBPNet) to gradually learn residual between the reconstructed face image and the ground truth by multi-step residual learning. Firstly, the reconstructed high-resolution feature map is projected to the original low-resolution feature space to generate low-resolution feature map (the projected low-resolution feature map). Secondly, the projected low-resolution feature map is subtracted by original feature map to generate low-resolution residual feature map. And finally, the low-resolution residual feature map is mapped to high-resolution feature space. The network will get a more accurate high-resolution image by iterative residual learning. Meanwhile, we explicitly reconstruct the edge map of face image and embed it into the reconstruction of high-resolution face image to reduce distortion of super-resolution results. Extensive experiments demonstrate the effectiveness and advantages of our proposed RBPNet qualitatively and quantitatively.