Recent researches demonstrate that correlation modeling plays a key role in high-performance multi-label classification methods. However, existing methods do not take full advantage of correlation information, especially correlations in feature and label spaces of each image, which limits the performance of correlation-based multi-label classification methods. With more correlations considered, in this study, a Fully Associative Network (FAN) is proposed for fully exploiting correlation information, which involves both visual feature and label correlations. Specifically, FAN introduces a robust covariance pooling to summarize convolution features as global image representation for capturing feature correlation in the multi-label task. Moreover, it constructs an effective label correlation matrix based on a re-weighted scheme, which is fed into a graph convolution network for capturing label correlation. Then, correlation between covariance representations (i.e., feature correlation ) and the outputs of GCN (i.e., label correlation) are modeled for final prediction. Experimental results on two datasets illustrate the effectiveness and efficiency of our proposed FAN compared with state-of-the-art methods.