A synchronous streak tube capable of providing high spatial resolution， high temporal resolution and large working area is numerically designed and experimentally demonstrated. In this paper， a 3-D model developed to systematically and comprehensively analyze the dependence of the physical temporal resolution on the accelerating voltage， the spatial resolution on the deflector-to-cathode distance， the dynamic spatial resolution and temporal resolution on the scanning velocity. Finally， geometry and electric parameters of d_DC=100 mm， U_g=700 V， and T_screen= 0.5 ns are proposed to optimize the streak tube performances. The numerical simulations show that the static spatial resolution is higher than 25 lp/mm @ MTF=10% and the dynamic spatial resolution is higher than 16 lp/mm @ MTF=10% over the whole effective photocathode area of 18 mm×2 mm. And， the simulated temporal resolution is better than 5.6 ps at T_screen=0.5 ns. Furthermore， the photocathode radiant sensitivity can reach 51 mA/W at the wavelength of 400 nm. The tested static spatial resolution is as high as 25 lp/mm @ CTF=13%.