Scannerless (flash) lidar system based on streak camera is able to realize three-dimensional (3D) multi-spectral fluorescence imaging and 3D imaging polarimetry. Compared with conventional lidar system, the flash lidar system overcomes image distortions caused by the motion between the target and the sensor platform. Other advantages of the flash lidar system are higher image update rates and the potential for creating a miniaturized lidar system. To meet the requirements for developing this new technology, a super small-sized, large photocathode area and meshless streak tube with spherical cathode and screen is designed with the aid of computer simulation technology (CST) software. The tube with nearly 28 mm wide photocathode work area contains two electrostatic focusing lens, a pair of deflection plates, and a 50 mm diameter output screen. The external dimension of the tube is merely 50 mm100 mm. And its electromagnetic fields are calculated in the CST Particle Studio based on the finite integration theory. Some dynamic properties of the tube are analyzed via observing different electron trajectories launched from a number of different points on the cathode. The influences of the deflector position on deflection sensitivity and spatial resolution are analyzed. Increasing the distance between the deflector and the anode pin hole leads to a worse deflection sensitivity but a better spatial resolution. As for the temporal resolution, three electron pulses separated by 30 ps can be well resolved by the streak tube in the dynamic mode. Thus, the dynamic temporal resolution of the streak tube is better than 30 ps. And a 10 lp/mm spatial resolution across the 28 mm long slit on the photocathode can be obtained by estimating modulation transfer functions of the electron trajectories. Temporal distortions at the entire photocathode working area are evaluated, and the data reveal that the larger the photocathode working area, the bigger the temporal distortions are. Also, the temporal distortion is present mainly in the photocathode-to-deflection plates region. In addition, the slit image of the streak tube working in the dynamic mode is simulated and presented. The phenomenon that the slit image is curved due to the temporal distortion is analyzed. Two rectangular electron pulses separated by 50 ps are well resolved by the streak tube. Therefore, the temporal resolution of this small-size steak tube is better than 50 ps with a rectangular slit dimension of 30 mm50 m on the photocathode, and its electron-optic magnification is 1.2.