This study aims to analyze the characteristics of micro-combustion and unsteady flame development in nitrate ester-plasticized polyether (NEPE) propellant when exposed to rapid pressure decay. A three-dimensional NEPE propellant combustion model is firstly established to achieve this goal. The framework consists of two parts. Firstly, we used sequential algorithms to generate a 3D numerical pack satisfying industrial requirements. In the numerically generated propellant pack, Ammonium perchlorate (AP) particles, and Cyclotetramethylene tetranitramine (HMX) particles are assumed as spheres, whereas the void space is Nitroglycerin/1,2,4-Butane triol trinitrate (NG/BTTN) binder. Secondly, a new kinetic model considering the pyrolysis of condensed phase and complicated interaction of gas species in the gas phase is proposed, which has been not reported until now. The accuracy of this framework is verified via comparing with experimental results. Upon simulating the depressurization combustion of NEPE propellant, it is observed that the non-planar surface stimulates the growth of Leading-Edge Flames, leading to intensified burning during the initial stage of depressurization combustion. After 5.2 ms of depressurization combustion, a remarkable increase in bulk heat release in the gas phase is discovered, attributed to the involvement of coarse AP particles, thereby providing a conducive oxidizing burning environment. Examination of the propellant surface temperature reveals that the oxidizer/binder interface exhibits higher temperatures ( 950 K) at 3.4 MPa, while the particle core typically remains cooler ( 850 K) at pressures ranging from 1.0 to 3.5 MPa. The dynamic temperature fluctuations are a result of the heterogeneity of the propellant microstructure, which also serves as the primary cause of oscillations in several globally averaged parameters. The flickering flame behavior during transient combustion, along with the corresponding combustion characteristics, offers theoretical insights for the study of combustion instability in solid rocket motors, warranting further validation through experimental cases.