The high resolution extreme ultraviolet spectroscopy mission based on the normal-incidence multilayered diffraction grating technology, which provides high effective area and spectral resolution, can carry out a survey of local Galactic stellar and white dwarf targets. Compared to grazing-incidence systems, this approach allows previous observatory-class science to be delivered in a low-cost package. The instrument has already been proven in two sub-orbital space flights. However, the multilayer used before is periodic one and the working band-pass is limited. In this paper, the spectroscopic properties of a normal-incidence multilayered diffraction grating were simulated with three kinds multilayers for the wavelength range between 17.5nm and 25.0nm, which includes lines of Fe VIII to XIII that will be strongest in the cooler (solar like) coronae, plus some weaker lines of O, Si, S and Ar. The highest efficiency at central wavelength of band-pass can be obtained if the periodic multilayer is adopted. The most flat response efficiency can be achieved if we utilized a non-periodic multilayer. The simulation results demonstrated that the choice of the multilayer is dependent on the requirement to the spectroscopy mission and should be considered carefully.