In this study, parametric cycle analysis of a conceptual turbojet engine with an afterburner (TJEAB) was conducted at sea level conditions-zero Mach. Based on this analysis, exergetic sustainability parameters of TJEAB were scrutinized for military mode (MM) and afterburner mode (ABM). Constitutively, several design parameters of TJEAB were chosen so as to optimize performance and exergetic parameters which consist of specific fuel consumption (SFC), overall efficiency, exergy efficiency, environmental effect factor (EEF) and exergetic sustainability index (ESI). In this context, compressor pressure ratio (CPR), turbine inlet temperature (TIT) were preferred due to high effect of these variables on engine performance. CPR ranges from 4 to 11 whereas TIT varies from 1150 K to 1550 K. According to optimization of performance parameters, minimum SFC was achieved as 28.59 g/kN.s at MM and 43.95 g/kN.s at ABM. On the other hand, maximum overall efficiency is determined as to be 13.07 % at MM and to be 8.5 % at ABM. As for exergetic parameters, exergy efficiency was calculated as maximum with 30.85 % at MM and 23.2 % at ABM. Finally, maximum exergetic sustainability index of TJEAB was computed as 0.446 at MM and 0.269 at ABM. It is thought that energetic and exergetic parameters analyzed in this analysis could guide in designing turbojet engines in terms of lower fuel consumption thereby environmental-benign.