The rapid development of facial recognition technology has brought great convenience to daily life, but also serious security risks, especially in the case of occlusion and loud noise. Faced with this limitation, this letter proposes a fast face recognition framework called a Group Sparse-based Discriminative Feature Learning (GSDFL-Net). Specifically, GSDFL-Net uses a novel unified objective function to simultaneously learn the discriminant features, sparse code and classification errors. In the proposed framework, the feature projection is incorporated into GSDFL-Net model, which reduces the classification errors. Then, we integrate denoising FFDNet into the proposed GS FL-Net model to penalize the noisy pixels, which is simultaneously learned by our unified objective function. Besides, we derive an optimization mechanism to encourage obtained learning parameters and decrease the information loss. Extensive experiments demonstrate the effectiveness of the proposed scheme under different including occlusion random noise conditions on the famous Aleix Martinez and ExYale B database.