We describe an astronomical 6U CubeSat mission VERTECS (Visible Extragalactic background RadiaTion Exploration by CubeSat). The scientific purpose of VERTECS is to reveal star-formation history of the universe by observation of the extragalactic background light (EBL) in visible wavelengths. Earlier observations by sounding rockets and infrared astronomical satellites have shown that the near-infrared EBL is several times brighter than the integrated light of known galaxies. As candidates for the excess light, first-generation stars in the early universe or low-redshift intra-halo light have been proposed, but it has not been concluded. Since these objects are expected to show different emission spectra in visible wavelengths, precise visible observation is important to reveal the origin of excess light. Since detection sensitivity of the EBL is determined by the product of telescope aperture and field of view, a small wide-field telescope system enables the EBL observation with high sensitivity. In VERTECS mission, we develop a 6U CubeSat equipped with a 3U size telescope optimized for observation of visible EBL. The telescope is composed of lens optics and a CMOS sensor of 3k times 3k array format, which is designed to observe the sky in four photometric bands in 400-800nm. The satellite bus is composed of on-board computer (OBC), electric power system (EPS), communication (COM), attitude determination and control system (ADCS), and thermal structure. Design of OBC and EPS is based on heritage of CubeSats developed at Kyushu Institute of Technology, but deployable solar array wings is added to EPS to supply sufficient power to perform the mission. In COM system, S-band is used for command uplink and X-band is used for high-speed downlink of large-size images captured by the telescope. Since the EBL measurement requires discrimination of the background light from discrete foreground stars, VERTECS requires 10 arcseconds pointing stability (1 sigma) in 1 minute exposure, which is critical and challenging requirements for VERTECS. In 2022, VERTECS was selected for JAXA-Small Satellite Rush Program (JAXA-SMASH Program), a new program that encourages universities, private companies and JAXA to collaborate to realize small satellite missions utilizing commercial small launch opportunities, and to diversify transportation services in Japan. We started the satellite development in December 2022. After design of the subsystems in 2023, we have been working on functionality and interface communication test using bread board model (BBM), as well as production of structure thermal model. We now plan to launch the FM satellite in 2025. We develop the satellite within about 2 years and obtain scientific results much more quickly than recent large astronomical-satellite missions.