In the field of cardiac magnetic resonance (MR) image analysis, the accurate segmentation of right ventricle (RV) regions plays an important role in the quantitative examination and medical diagnosis of various cardiovascular diseases. However, the automated RV segmentation in cardiac MR images is still challenging, due to its obscure and ill-defined boundaries, variably crescent-shaped structures, and extremely-unbalanced area ratio between the RV region and the background. In this work, an edge feature-induced self-attention multi-scale feature aggregation full convolutional neural network, called EFiSaMsFAFUnet, is proposed, to address the RV segmentation tasks. Specifically, EFiSaMsFAFUnet introduces an edge feature extraction module (EFEM) to mine the crescent-shaped boundary features of the RV area, and a kind of self-attention multi-scale feature expansion block (SaMsFEB) is proposed to mine the internal structure characteristics of the crescent-shaped RV internal regions. In addition, a kind of composite loss function is used to address the problem of model degradation caused by the proportion imbalance between RV region and background. The proposed EFiSaMsFAFUnet was evaluated on the MICCAI2017 Automatic Cardiac Diagnosis Challenge (ACDC) dataset. Extensive confirmatory and comparative experiments show that the EFiSaMsFAFUnet can achieve better segmentation results than the representatively state-of-the-art methods, and it can achieve comparable or the closest segmentation results to the manual segmentation of clinical specialist.