The performance of traditional face recognition systems is sharply reduced when encountered with a low-resolution (LR) probe face image. To obtain much more detailed facial features, some face super-resolution (SR) methods have been proposed in the past decade. The basic idea of a face image SR is to generate a high-resolution (HR) face image from an LR one with the help of a set of training examples. It aims at transcending the limitations of optical imaging systems. In this paper, we regard face image SR as an image interpolation problem for domain-specific images. A missing intensity interpolation method based on smooth regression with a local structure prior (LSP), named SRLSP for short, is presented. In order to interpolate the missing intensities in a target HR image, we assume that face image patches at the same position share similar local structures, and use smooth regression to learn the relationship between LR pixels and missing HR pixels of one position patch. Performance comparison with the state-of-the-art SR algorithms on two public face databases and some real-world images shows the effectiveness of the proposed method for a face image SR in general. In addition, we conduct a face recognition experiment on the extended Yale-B face database based on the super-resolved HR faces. Experimental results clearly validate the advantages of our proposed SR method over the state-of-the-art SR methods in face recognition application.