The sun is the main source of Earth's energy. As such solar activity and changes have a great influence on the Earth. To meet the solar observation and research needs of astronomers, a new type of Lyman alpha and visible dual-band internal occulting coronagraph was designed to meet the needs of high-resolution imaging observation of the corona at 121.6 nm and 700 nm for space. Firstly, the parameters of the instrument were determined according to the radiation characteristics of the solar disc and corona in the 121.6 nm and 700 nm bands and the initial structure of the coronagraph was given. The initial structure was optimized by an evaluation function. The imaging performance of the coronagraph optics was calculated and the influence of various optical elements on stray light was analyzed. The main optical components and mechanical structure affecting stray light were determined and the position and surface treatment method of a Lyot stop were designed. The coating film structure of the optical components and optical chromoscope of the coronagraph were designed to achieve simultaneous imaging in the 121.6 nm and 700 nm bands. The design and analysis results show that the field of view (FOV) of the coronagraph covers a 1.1 (Rs=0.267 degrees) to 2.5 solar radius, the effective focal length of the system is 945 mm, the spot radius root mean square (RMS) of the entire field of view is less than 10 um, and the angular resolution is better than 4.8 arcsec. The stray light suppression level of the system is better than 10-6 at 1.1 Rs and 10-8 at 2.5 Rs.