Nitrate ester plasticized polyether (NEPE) propellant is widely used in solid rocket motors, having both good mechanical properties and high specific impulse. However, its ignition and combustion process are complex and need to be better understood. In this study, a high-pressure sealed combustion chamber was constructed, a thermogravimetry-differential scanning calorimetry was used to investigate the thermal decomposition process, and a high-speed camera was used to capture the ignition process and combustion behavior of the propellant. The results showed that the thermal decomposition process of this propellant could be divided into two stages. The first stage (50–350°C) was the major mass loss stage and exhibited typical features of BTTN, RDX, and AP decomposition. The second stage (350–500°C) was mainly accompanied by decomposition of the remaining components as well as slight oxidation of aluminum particles. The ignition process of NEPE propellant was divided into four stages, including the inert heating period stage, thermal decomposition stage, initial flame stage, and stable combustion stage. After the propellant absorbed heat, the propellant started to pyrolyze and gasify to generate flammable gas. When the temperature of the propellant surface reached the flammable gas ignition point, an initial flame was generated on the surface, which spread rapidly, covering the surface. The ignition delay time of the propellant was measured by a signal acquisition system, and a mathematical model was then established for the ignition delay time. The results showed that the ignition delay time decreased with increased laser heat flux and ambient pressure. Finally, the Vielle burning rate empirical formula was used to fit the burning rate data for the propellant. The resulting good fit was consistent with experimental measurements and showed that the formula was valid for predicting the NEPE propellant burning rate under 0.1–3.0 MPa nitrogen.