Recently, the locality linear coding (LLC) has attracted more and more attentions in the areas of image processing and computer vision. However, the conventional LLC with real setting is just designed for the grayscale image. For the color image, it usually treats each color channel individually or encodes the monochrome image by concatenating all the color channels, which ignores the correlations among different channels. In this paper, we propose a quaternion-based locality-constrained coding (QLC) model for color face hallucination in the quaternion space. In QLC, the face images are represented as quaternion matrices. By transforming the channel images into an orthogonal feature space and encoding the coefficients in the quaternion domain, the proposed QLC is expected to learn the advantages of both quaternion algebra and locality coding scheme. Hence, the QLC cannot only expose the true topology of image patch manifold but also preserve the inherent correlations among different color channels. Experimental results demonstrated that our proposed QLC method achieved superior performance in color face hallucination compared with other state-of-the-art methods.