The observation of solar spectral imaging provides an importance data source for solar physics and space weather research. However, it faces a serious challenge from the dynamic solar atmosphere in the extreme ultraviolet (EUV) band. Only by time-consuming push-broom imaging can the traditional slit-type imaging spectrometer acquire 2D images of the solar disk due to a limited instantaneous field of view (FOV). Moreover, its system is unable to capture the rapid evolution of the solar transition region and corona since it does not have a high time resolution. Although an EUV imager can observe at a large 2D FOV and high time resolution, it cannot get the spectral resolution. For this reason, relying on the aberration-corrected elliptical varied line-space (EVLS) grating, we proposed a new slitless imaging spectrometer in this paper, which can simultaneously work in three diffraction orders (m=-1, 0, or +1). Besides, three EUV narrowband (29.4--31.4 nm) images of the solar disk with a FOV of 20 arcmin×20 arcmin can be obtained in a single snapshot without the mechanical motion of any component, which demonstrates the high time resolution and large FOV of our instrument. Additionally, the zero-order system without spectral dispersion, equivalent to an EUV imager, can directly obtain high-resolution spatial information (0.6 arcsec). In contrast, the images from the ±1-order systems with spectral dispersion carry spatial and spectral overlapping information, which is similar to the imaging principle of computed tomography. High-resolution spectral information (0.0035 nm) can be extracted from the 3-order images by a data inversion algorithm.