Image deblurring is an essential problem in computer vision. Due to highly structured and special facial components (e.g. eyes), most general image deblurring methods and face deblurring methods failed to yield more explicit structure and facial details, resulting in too smooth, uncoordinated and distorted face structure. Considering the unique face texture and sufficient facial details, we present an effective face deblurring network by exploiting more regularized structure and enhanced texture information (RSETNet). We first incorporate the face parsing network with fine-tuning to obtain more accurate face structure, and we present the feature adaptive denormalization (FAD) to regularize the facial structure as a condition of auxiliary to generate more harmonious and undistorted face structure. Meanwhile, to improve the generated facial texture information, we propose a new Laplace depth-wise separable convolution (LDConv) and multi-patch discriminator. Compared with existing methods, our face deblurring method could restore face structure more accurately and with more facial details. Experiments on two public face datasets have demonstrated the effectiveness of our proposed methods in terms of qualitative and quantitative indicators.