For the research of solar EUV (extreme ultraviolet) radiation, we have designed a small-sifted engineering model of solar EUV telescope, which is suitable for a Korean satellite. The EUV sole. telescope was designed to observe the sun at $584.3AA$(He I) and $629.7AA$(OV) The optical system is an f/8 Ritchey-Chr rien, and the effective diameter and focal length are 80mm and 640mm, respectively. The He I and 0V filters are loaded in a filter wheel. In the detection part, the MCP (Microchannel Plate) type is Z-stack, and the channel-to-diameter radio is 40:1. MCP and CCD are connected by fiber optic taper. A commercial optical design software is used for the analysis of the optical system design.