In order to study the effects of strain rate and tensile-shear angle on the tensile-shear strength of NEPE propellant， tensile-shear tests of the propellant for 5 tensile-shear angles （0°， 30°， 45°， 60°， 90°） and 5 strain rates （0.0012， 0.0048， 0.024， 0.12， 1 s^-1） were carried out by using tensile-shear fixtures and butterfly test specimens. The variation of tensile-shear strength with tensile-shear angle and strain rate of propellant under combined tensile-shear loading was obtained. Based on the experimental results， the tensile-shear strength limit of propellant was described by the improved circular equation， and the tensile-shear strength criterion of propellant at different strain rates was established by combining the double shear unified strength theory， and the corresponding theoretical limit surface of the unified strength of propellant was drawn. Finally， the established tensile-shear strength criterion was used to predict the tensile-shear strengths of 0.12 s^-1 and 1 s^-1 strain rates for the tensile-shear angles of 15° and 75°. The validity of the established tensile-shear strength criterion was verified by comparing the predicted results with the experimental data. The results show that the tensile-shear strength of NEPE propellant under combined tensile-shear load increases with the increase of tensile-shear angle and strain rate. By fitting and solving the material parameter values， the improved circular equation and unified strength criterion established can well describe the tensile-shear strength of NEPE propellant for different loading angles and strain rates. Based on the established strength criterion， the errors between the predicted values and the experimental values of the tensile strength limits at the strain rates of 0.12 s^-1 and 1 s^-1 for the tensile-shear angles of 15° and 75° are less than the allowable error range of the actual treatment by 15%.