Glycidylazide polymer (GAP) has potential interest for the development of high-performance energetic propellants. Although GAP is a well-known and promising energetic polymer, propellants based on it suffer from poor mechanical and low-temperature properties. In order to improve the mechanical and thermal properties of GAP a promising idea would be the preparation of a triblock copolymer of it with a polymer having good mechanical and thermal properties, such as polycaprolactone (PCL). In this work, we report a detailed investigation of the glass transition temperature (Tg) and viscosity of PCL-GAP-PCL samples incorporated with energetic plasticizers, BuNENA, TMETN, and BTTN. The results demonstrated that the Tg of PCL-GAP-PCL is influenced by the type of plasticizer. PCL-GAP-PCL was cured with TDI and a mixed curing system (IPDI/N100). The elastomer prepared with the mixing curing system showed excellent mechanical properties with 2.64 MPa and 138% elongation. The effects of the energetic plasticizers on the mechanical properties of the elastomer were investigated. Finally, the plasticized tri-block copolymer showed enhanced mechanical and thermal properties.