Heterogeneous face recognition (HFR) refers to matching face images acquired from different domains with wide applications in security scenarios. However, HFR is still a challenging problem due to the significant cross-domain discrepancy and the lacking of sufficient training data in different domains. This paper presents a deep neural network approach namely Multi-Margin based Decorrelation Learning (MMDL) to extract decorrelation representations in a hyperspherical space for cross-domain face images. The proposed framework can be divided into two components: heterogeneous representation network and decorrelation representation learning. First, we employ a large scale of accessible visual face images to train heterogeneous representation network. The decorrelation layer projects the output of the first component into decorrelation latent subspace and obtain decorrelation representation. In addition, we design a multi-margin loss (MML), which consists of tetradmargin loss (TML) and heterogeneous angular margin loss (HAML), to constrain the proposed framework. Experimental results on two challenging heterogeneous face databases show that our approach achieves superior performance on both verification and recognition tasks, comparing with state-of-the-art methods.