Face hallucination is a domain-specific super-resolution (SR), that generates high-resolution (HR) facial images from the observed one/multiple low-resolution (LR) input/s. Recently, convolutional neural networks(CNNs) are successfully applied into face hallucination to model the complex nonlinear mapping between HR and LR images. Although global attention mechanism equipped into CNNs naturally focus on the facial structure information, it always ignore the local and cross feature structure information, resulting in limited reconstruction performance. In order to solve this problem, we propose global-local split-attention mechanism and design a Split-Attention in Split-Attention (SIS) network to enable local attention across feature-map groups attaining global attention and to improve the ability of feature representations. SIS can generate and focus the local attention of neural network on the interaction of face key structure information in channel-level, thereby improve the performance of face image reconstruction. Experimental results show that the proposed approach consistently and significantly improves the reconstruction performances for face hallucination.