The electron-optical model of high dynamic range anisotropic focusing streak tube is built. Via calculating the electric field distribution and tracking electron beam trajectory of the whole system, high voltage electrodes which may trigger the electric sparks are analyzed; the effect of electric quadrupole lens on the streak tube magnification, static and dynamic image quality are studied; the temporal distortion is calculated. The results show that the temporal distortion in the 20 mm long slit is only 15 ps, in which the variation of the ramp voltage imposed on the deflectors is as small as 3.06 V. Thus, the slit image distortion caused by the temporal distortion can be ignored. The optimum time resolution of 1.8 ps and dynamic range of 1 000∶1 at temporal resolution of 8 ps are successfully demonstrated in the experiments.