In the process of investigating a case, face image is the most interesting clue. However, due to the limitations of the imaging conditions and the low-cost camera, the captured face images are often Low-Resolution (LR), which cannot be used for criminal investigation. Face image super-resolution is the technology of inducing a High-Resolution (HR) face image from the observed LR face image. It has been a topic of wide concern recently. In this paper, we propose a novel face image super-resolution method based on Tikhonov Regularized Neighbor Representation, which is called TRNR for short. It can overcome the technological bottlenecks (e.g., instable solution) of the patch representation problem in traditional neighbor embedding based image super-resolution method. Specially, we introduce the Tikhonov regularization term to regularize the representation of the observation LR patch, which can give rise to a unique and stable solution for the least squares problem and produce detailed and discriminant HR faces. Extensive experiments on face image super-resolution are carried out to validate the generality, effectiveness, and robustness of the proposed algorithm. Experimental results on the public FEI face database show that the proposed method plays a better subjective and objective performance, which can recover more fine structures and details from an input low-resolution image, when compared to previously reported methods.