The structure and principle of an optically written display based on up-conversion of near infrared light is presented. In order to improve the screen luminance and avoid the leakage of infrared light,two multi-layer interference filters are designed for the display. One is called LP filter,which has low transmittance for visible light between 420～800 nm,and a high transmittance for infrared light between 800～1000 nm;The other is called SP filters with opposite characteristics. Layer-symmetric films are used to design the filters and MATLAB is used to simulate and optimize the design. The obtained LP and SP filters have good characteristics within the whole wavelength bandwidth and the incident angles of 0°～30°. The 21-layer LP and SP filters have a total thickness of 1586.8 nm and 2157.8 nm,respectively. The manufacturing tolerances on material refractive index and film thickness are reasonably large.