Luminal-A breast cancer is the most frequently occurring subtype which is characterized by high expression levels of hormone receptors. However, some luminal-A breast cancer patients suffer from intrinsic and/or acquired resistance to endocrine therapies which are considered as first-line treatments for luminal-A breast cancer. This heterogeneity within luminal-A breast cancer has required a more precise stratification method. Hence, our study aims to identify prognostic subgroups of luminal-A breast cancer. In this study, we discovered two prognostic subgroups of luminal-A breast cancer (BPS-LumA and WPS-LumA) using deep autoencoders and gene expressions. The deep autoencoders were trained using gene expression profiles of 679 luminal-A breast cancer samples in the METABRIC dataset. Then, latent features of each samples generated from the deep autoencoders were used for K-Means clustering to divide the samples into two subgroups, and Kaplan-Meier survival analysis was performed to compare prognosis (recurrence-free survival) between them. As a result, the prognosis between the two subgroups were significantly different (p-value = 5.82E-05; log-rank test). This prognostic difference between two subgroups was validated using gene expression profiles of 415 luminal-A breast cancer samples in the TCGA BRCA dataset (p-value = 0.004; log-rank test). Notably, the latent features were superior to the gene expression profiles and traditional dimensionality reduction method in terms of discovering the prognostic subgroups. Lastly, we discovered that ribosome-related biological functions could be potentially associated with the prognostic difference between them using differentially expressed genes and co-expression network analysis. Our stratification method can be contributed to understanding a complexity of luminal-A breast cancer and providing a personalized medicine.