Diabetes is one of the most common disease in individuals. Diabetic retinopathy (DR) is a complication of diabetes, which could lead to blindness. Automatic DR grading based on retinal images provides a great diagnostic and prognostic value for treatment planning. However, the subtle differences among severity levels make it difficult to capture important features using conventional methods. To alleviate the problems, a new deep learning architecture for robust DR grading is proposed, referred to as SEA-Net, in which, spatial attention and channel attention are alternatively carried out and boosted with each other, improving the classification performance. In addition, a hybrid loss function is proposed to further maximize the inter-class distance and reduce the intra-class variability. Experimental results have shown the effectiveness of the proposed architecture.