Based on the small-size streak tube, the dependence of the physical temporal resolution and temporal distortion on the factors including initial energy of electrons generated from the photocathode and spherical photocathode curvature radius is numerically simulated. The simulation results show that the physical temporal resolution is greatly affected by the initial energy, which is less affected by the spherical curvature radius and off-axis distance; the temporal distortion increases with the off-axis distance. Furthermore, the streak tube with a flat photocathode has a positive temporal distortion. With the decrease of the radius of curvature of the photocathode, the temporal distortion gradually changes from positive value to negative ones. And, when the photocathode curvature radius is 70 mm, the temporal distortion can be reduced to 8 ps and the spatial resolution can reach 25 lp/mm @ MTF=10%, the curvature of the slit image can be almost neglected even though the off-axis distance is 8 mm. Besides, the static spatial resolution and luminance gain of the streak tube, the luminance photocathode sensitivity of the photocathode are tested experimentally. The experiment results show that the spatial resolution of the streak tube is higher than 28 lp/mm at the photocathode center while it is higher than 18 lp/mm at the edge. The luminance photocathode sensitivity of the small-size streak tube is 178 μA/lm and the luminance gain is higher than 12 while the luminance gain of picosecond streak tube is only 0.5. Thus, the small-size streak tube has a good weak light detection ability in the field of streak tube imaging lidar.