Fair representation learning aims to encode invariant representation with respect to the protected attribute, such as gender or age. In this paper, we design Fairness-aware Disentangling Variational AutoEncoder (FD-VAE) for fair representation learning. This network disentangles latent space into three subspaces with a decorrelation loss that encourages each subspace to contain independent information: 1) target attribute information, 2) protected attribute information, 3) mutual attribute information. After the representation learning, this disentangled representation is leveraged for fairer downstream classification by excluding the subspace with the protected attribute information. We demonstrate the effectiveness of our model through extensive experiments on CelebA and UTK Face datasets. Our method outperforms the previous state-of-the-art method by large margins in terms of equal opportunity and equalized odds.