The transport process of a relativistic electron beam (REB) in high density and degenerate plasmas holds significant importance for fast ignition. In this study, we have formulated a comprehensive theoretical model to address this issue, incorporating quantum degeneracy, charged particle collisions, and effects of electromagnetic (EB) fields. We model the fuel as a uniform density region and specially focus on the effect of quantum degeneracy during the transport of the REB, which leads to the rapid growth of self-generated EB field and a subsequently significant self-organized pinching of the REB. Through our newly developed hybrid particle-in-cell simulations, we have observed a two-fold enhancement of the heating efficiency of REB than previous intuitive expectation. This finding provides a promising theoretical framework for exploring the degeneracy effect and the enhanced self-generated EB field in the dense plasma for fast ignition, and is also linked to a wide array of ultra-intense laser-based applications.