Based on a plastic scintillator and an optic streak camera, a measuring system for fusion reaction-rate was designed, then the working princile and design method of the measuring system were addressed in detail. A piece of fused silica window was set just behind the plastic scintillator to protect optical elements from darkening after a long time exposure in scatted X rays and the ultraviolet crystals and other ultraviolet glass were selected to ensure the high system transmission. Furthermore, the image plane of the optical system was put onto a photocathode of the streak camera directly to remove the aperture non-matching of input optic system of the streak camera. Finally, a field mirror was put on the first image plane to reduce the max diameter of optical element from 160 mm to 120 mm. The designed optical system has a total length of 2 660 mm, magnification of 3∶1 and its final lens is F/0.667 and transmission is 67%. Moreover, the time dispersion of the optical system is less than 7.3 ps. These results meet the experimental needs of different neutron yields and good experimental results have been obtained in a laser targeting experiment.