Recently, the face hallucination method based on deep learning understands the mapping between low-resolution (LR) and high-resolution (HR) facial patterns by exploring the priors of facial structure. However, how to maintain the face structure consistency after the reconstruction of face images at different scales is still a challenging problem. In this letter, we propose a novel multi-scale structure prior learning (MSPL) for face hallucination. First, we propose a multi-scale structure prior block (MSPB). Considering the loss of high-frequency information in the LR space, we mainly process the input image in three different scale ascending dimensional spaces, and map the image to the high dimensional space to extract multi-scale structural prior information. Then the size of feature maps is recovered by downsampling, and finally the multi-scale information is fused to restore the feature channels. On this basis, we propose a local detail attention module (LDAM) to focus on the local texture information of faces. We conduct extensive face hallucination reconstruction experiments on a public face dataset (LFW) to verify the effectiveness of our method.