In recent years, there are numerous works been proposed to leverage the techniques of deep learning to improve social-aware recommendation performance. In most cases, it requires a larger number of data to train a robust deep learning model, which contains a lot of parameters to fit training data. However, both data of user ratings and social networks are facing critical sparse problem, which makes it not easy to train a robust deep neural networkmodel. Towards this problem, we propose a novel correlative denoising autoencoder (CoDAE) method by taking correlations between users with multiple roles into account to learn robust representations from sparse inputs of ratings and social networks for recommendation. We develop the CoDAE model by utilizing three separated autoencoders to learn user featureswith roles of rater, truster and trustee, respectively. Especially, on account of that each input unit of user vectors with roles of truster and trustee is corresponding to a particular user, we propose to utilize shared parameters to learn common information of the units that corresponding to same users. Moreover, we propose a related regularization term to learn correlations between user features that learnt by the three subnetworks of CoDAE model. We further conduct a series of experiments to evaluate the proposed method on two public datasets for Top-N recommendation task. The experimental results demonstrate that the proposed model outperforms state-of-the-art algorithms on rank-sensitive metrics of MAP and NDCG.