Extreme Ultraviolet (EUV) spectroscopic observation is one of the most important approaches in diagnosing the basic physical phenomena in the solar atmosphere. However, the designs of many instruments used for visible wavelengths cannot be applied for EUV because of its much shorter wavelength. Conventional solar EUV imagers and spectrographs have their own limitations: Where as we cannot get spectral information from a EUV imager, it takes too long time for a single slit spectrometer to scan an area, which makes it difficult to catch the dynamics of highly transient solar activities. These limitations make the high resolution observation of solar activities and the research of its mechanism very difficult. We cannot observe the acceleration process of CME (coronal mass ejections) in inner coronal and cannot connect the CME observed by visible light with the activity area observed by EUV directly. Moreover, we cannot get the line-of-sight velocity of the solar activities, so it is difficult to find the source area of CME. In this paper, we present the design of a new type of solar EUV spectral imager with extra high spectral resolution. It can get the full-disk EUV image of the Sun with additional information on spectral line profile. So we can get the line-of-sight velocity of plasma in low coronal and the velocity map of the full coronal disk. Combining the spatial and spectral information, we can identify the movement corresponding to the configuration evolvement of the plasma. Because there is no slit and movement assembly, the imager can get high temporal resolution data of the whole solar disk to capture the rapidly transformation of solar activities. The new imager adopts a kind of slitless spectral imaging design, which means to project a narrow band spectrum data from different angle to a plate detector and invert to get the spatial image and spectral information. The biggest difference between the multi-order spectral imaging and the traditional spectrograph is that there is no scanning slit in former. These give the new imager the advantage which can get the spatial and spectral information in a wide field of view simultaneously. Considering the limitations of the EUV band and space application, it is impossible to get many orders image like the medical CT or telescopes response to visible light. Based on the multi-order imager principle, we proposed a five-order spectrograph. The optical system of the new imager consists of a reflect mirror, a grating and five CCD detectors. The dispersed lights after the grating are received by five detectors. Four detectors receive ±1 and ±2 orders of diffraction, and another one receives 0 order image with spatial resolution information. The spectral information can be obtained by inversion with five orders spectral images. The paper introduces the design of the optical system based on a varied line space (VLS) grating and the inversion algorithm, which will improve the instrument efficiency and image qualitywith limited volume and weight. The spatial resolution will be 1.8 arcsec·pixel-1 and the spectral resolution will be 7.8×10-3 nm·pixel-1. With this technology, we can get the full solar disk velocity map aswell as the intensity map simultaneously, which is suitable for space application.