Abstract: First, a modified stencil approximation method is introduced, which improves the second-order polynomial approximation of the numerical flux on each candidate sub-stencil in the classical fifth-order WENO-JS scheme. The stencil approximation reaches the fourth-order accuracy by adding a cubic correction term, and it has ENO property by introducing an adjustable function.Then the modified stencil approximation method is applied to WENO-Z+and WENO-Z+M schemes, and the modified WENO-Z+schemes based on the modified stencil type (WENO-MS-Z+, WENO-MS-Z+M) are developed.A series of numerical examples are used to test the new schemes. The results show that the new schemes have a strong ability to capture shock waves and high resolution for small-scale wave structures, which is significantly improved compared with the original WENO-Z+and WENO-Z+M schemes.