Owing to the characteristics of high frame frequency, large field of view, small size, streak tube with large work area and small size has been the essential component of the streak tube imaging lidar, and has immense potential in the field of aerospace, space exploration and underwater detection. In this paper, streak tube with a large spherically curved photocathode and small size has been modeled and simulated. The static temporal resolution reaches to 633fs when the effective working diameter of photocathode is 28mm, and its magnification of the image is 1.4. The quantitative relationship between the curvature radius and temporal distortion is analyzed, and temporal distortion can be compensated to minimum when curvature radium R=45mm. Guidance is provided for developing a femtosecond streak tube with large work area and small size for 3D imaging lidar. © 2019 SPIE.