The relatively poor mechanical properties of extruded modified double base (EMDB) propellants limit their range of applications. To overcome these drawbacks, a novel method was proposed to introduce glycidyl azide polymer-based energetic thermoplastic elastomers (GAP-ETPE) with bonding groups into the propellant adhesive. The influence of the molecular structure of three kinds of elastomers on the mechanical properties of the resultant propellant was analyzed. It was found that the mechanical properties of the propellant with 3% CBA-ETPE (a type of GAP-ETPE that features chain extensions using N-(2-Cyanoethyl) diethanolamine and 1,4-butanediol) were improved at both 50 °C and -40 °C compared to a control propellant without GAP-ETPE. The elongation and impact strength of the propellant at -40 °C were 7.49% and 6.58 MPa, respectively, while the impact strength and maximum tensile strength of the propellant at 50 °C reached 21.1 MPa and 1.19 MPa, respectively. In addition, all three types of GAP-ETPE improved the safety of EMDB propellants. The friction sensitivity of the propellant with 3% CBA-ETPE was found to be 0%, and its characteristic drop height H50 was found to be 39.0 cm; 126% higher than the traditional EMDB propellant. These results provide guidance for studies aiming to optimize the performance of EMDB propellants.