The streak tube imaging lidar (STIL) community requires the streak tube with characteristics of small-size, high edge spatial resolution, high luminance gain, and large working area. In this work, with the aid of the computer simulation technology software, a streak camera with high edge spatial resolution and high luminance gain is designed, in which there are adopted 1) a spherical photocathode and screen to increase the edge spatial resolution and detection area, further enlarging the field of view for the STIL; 2) a slit accelerating electrode instead of the mesh one favorable for improving the electrical resistance and reliability for streak camera; 3) a streak tube with lower magnification combining with -15 kV working voltage to be able to achieve high luminance gain, thus further increasing the detection distance for STIL. Some static and dynamic properties of the tube are analyzed by observing different electron trajectories emitted from a number of different points on the photocathode. As for the spatial resolution, spatial modulation transfer function method is used to evaluate the spatial resolution characteristics of the streak tube. The 36.9 lp/mm at MTF=5% in static mode and 23 lp/mm at MTF=5% in dynamic mode of the high resolution across the 16 mm long slit on the photocathode can be obtained. As for the temporal resolution, three electron pulses at intervals of 54.6 ps can be well resolved by the streak tube in the dynamic mode. Thus, the temporal resolution of the streak tube is better than 54.6 ps. Furthermore, the influence of shape of the photocathode and screen on spatial resolution are analyzed. Compared with the P-streak tube (streak tube with plane photocathode and plane screen), S-streak tube (steak tube with spherical photocathode and spherical screen) can greatly improve the spatial resolution. The slit image of the spherical and plane photocathode are simulated. The spatial dispersion of the off-axis 8 mm slit image along the scanning direction is analyzed. The experimental results demonstrate that the spatial resolution of the small-size streak tube is 29.3 lp/mm at MTF=5% over the whole working area 16 mm2 mm, and the luminance gain is higher than 39.4. The static spatial resolution of the small-size streak tube is much higher than 15 lp/mm at CTF = 11.64%; the dynamic spatial resolution is higher than 9.8 lp/mm at CTF=5.51%; the temporal resolution is higher than 54.6 ps at Tscreen=4.3 ns and has good consistency on the whole photocathode, and the dynamic range is 345:1 at 54.6 ps. The streak camera contains 6 scanning levels for different depth of field and detection accuracy to achieve ultrafast signal diagnosis at different scanning speeds. The streak tube has a smaller dimension of 40 mm140 mm. It is of great significance in unmanned aerial and spaceborne laser imaging lidar detection.