Noise in hyperspectral images (HSIs) may degrade the HSI classification result. Robust principal component analysis (RPCA) is an excellent method to obtain low-rank (LR) representation of data and is widely used in image denoising and also in HSI classification. However, data are drawn as a union from multiple subspaces in HSIs, so LR subspace estimation (LRSE) is necessary when using RPCA, which is complicated and time-consuming. To solve this problem, this letter proposes a novel LR-based method for HSI classification called two-branch network combined with RPCA, which combines RPCA with a neural network. Specifically, both the LR component and the sparse component are preserved and used for feature extraction in two independent convolutional branches. This way, we can avoid information loss without using accurate LRSE. A concatenate operation and a pointwise convolution are then adopted to realize the feature fusion. Finally, fused features are constructed to indicate the ground truth of each pixel in the classification process. The proposed method constructs a convenient model for HSI classification by discarding the LRSE and combining denoising, feature extraction, feature fusion, and classification into an end-to-end network. The experimental results on three data sets demonstrate that the proposed method outperforms many state-of-the-art methods including ones based on LR representation and ones based on deep learning. In addition, it maintains good classification performance for the cases of small samples and class imbalance.