Cross-modal matching has recently drawn much attention due to the widespread existence of multimodal data. It aims to match data from different modalities, and generally involves two basic problems: the measure of relevance and coupled feature selection. Most previous works mainly focus on solving the first problem. In this paper, we propose a novel coupled linear regression framework to deal with both problems. Our method learns two projection matrices to map multimodal data into a common feature space, in which cross-modal data matching can be performed. And in the learning procedure, the 21-norm penalties are imposed on the two projection matrices separately, which leads to select relevant and discriminative features from coupled feature spaces simultaneously. A trace norm is further imposed on the projected data as a low-rank constraint, which enhances the relevance of different modal data with connections. We also present an iterative algorithm based on halfquadratic minimization to solve the proposed regularized linear regression problem. The experimental results on two challenging cross-modal datasets demonstrate that the proposed method outperforms the state-of-the-art approaches.