A small-size streak tube with electrostatic focusing lens is designed with the aid of three-dimensional electromagnetic simulation software, CST. Distances between electrodes of the streak tube and their voltages are determined by orthogonal experiments. Also, according to the aberration theory of the streak tube, its imaging qualities are analyzed and evaluated systematically. The optimal streak tube possesses predominant performances. The diameter of work area of the photocathode is larger than 28 mm; physical temporal resolution is better than 30 ps; static spatial resolution at the margin of the photocathode is greater than 20 lp/mm; electron- optical magnification of the tube is 1.07; overall length of the streak tube is only 100 mm; outer diameter of streak tube is 50 mm. The designed streak tube with large work area and small size meets the requirements of scannerless lidar systems in the applications of military imaging scenarios, space exploration and marine detection.