Face image super-resolution (FSR) algorithms are capable of providing a high-resolution image from an input low-resolution (LR) image. Various FSR algorithms use a set of training examples to reconstruct the input LR image. For the purpose, proper weights need to be calculated for each training image. In general, the least square estimation approach is used for obtaining optimal reconstruction weights, known as least square representation (LSR) problem. In this paper, to minimize LSR problem more effectively, a grey wolf optimizer (GWO) based FSR algorithm (FSR-GWO) is proposed. To make search process of GWO algorithm suitable to FSR, a new formulation for upper-bound and lower-bound is introduced. Performance comparison with state-of-the-art nature-inspired algorithms and several super-resolution methods on FEI public face database shows the effectiveness of the proposed FSR-GWO algorithm.