The Image Air shower Cherenkov Telescope (IACT) is one powerful instrument to study gamma ray astronomy. Generally the reflection system of IACT is assembled by multiple small sub-mirrors. It is time-consuming and costly to measure the sub-mirrors for the traditional manual method. In order to solve the problem, we design and develop an automatic system to measure the radius of curvature (ROC) of spherical sub-mirrors. A foam aluminum sample spherical mirror is tested to verify system performance. The repeated measurement error of the system ROC is 5.68 mm with the step 5 mm, and the minimum spot size repeated measurement error is 0.04 mm. The results indicate that the accuracy and stability of the system are excellent. Two mirrors with different ROC are measured. The ROC of the aluminum foam structure mirror is 16100.30 ± 5.59 mm, and the minimum spot size is 3.37 ± 0.04 mm. The ROC of a glass mirror is 5810.00 ± 1.42 mm with the step 1 mm and a minimum spot size of 1.92 ± 0.02 mm. The results indicate that the system is suitable for measuring mirrors with different ROCs and the measurement results are effective and reliable. It is vital to note that the measurement is fast and unattended, the single measurement time is less than 5 minutes and the total time is less than 15 minutes.