This paper reports the facile preparation, mechanical performance and linear viscoelasticity of polyetheramine-cured rubber-like epoxy asphalt composites (EACs) with different asphalt contents. Compared with previous EACs prepared via complex chemical reactions and time-consuming high-temperature curing, the EACs reported here were obtained by using a compatible, bi-functional polyetheramine and a simple physical co-blend process, which make the EACs feasibly scalable for production at a lower cost. The EACs were cured for 1 h at 160 °C and 3 d at 60 °C; therefore, these composites can be opened to traffic immediately. The EACs have a much greater temperature stability than common thermoplastic polymer-modified asphalt composites from −30 °C to 120 °C, but their complex shear moduli at higher temperatures slightly decrease instead of remaining constant when temperatures are greater than 80 °C, especially for the higher asphalt content composites; that is, these composites are quasi-thermosetting. Wicket plots illustrate that the EACs reported here are thermorheological simple materials, and the master curves are constructed and well-fitted by generalized logistic sigmoidal model functions. This research provides a facile, low-cost method for the preparation of polyetheramine-cured EACs that can be opened to traffic immediately, and the concept of quasi-thermosetting may facilitate the development of cheaper EACs for advanced applications.