In the line of sight correction system, the response time of the liquid crystal spatial light modulator under the normal driving voltage is too long to affect system performance. On the issues, an overdriving method based on a Field-Programmable Gate Array (FPGA) is established. The principle of the overdrive is to use a higher voltage difference to achieve a faster response speed of liquid crystal. In this scheme, the overdriving look-up table is used to seek the response time of the quantized phase, and the liquid crystal electrode is driven by Pulse-Width Modulation (PWM). All the processes are performed in FPGA, which releases the central processing unit (CPU) memory and responds faster. Adequate simulations and experiments are introduced to demonstrate the proposed method. The overdriving experiment shows that the rising response time is reduced from 530 ms to 34 ms, and the falling time is from 360 ms to 38 ms under the overdriving voltage. Typical light tracks are imitated to evaluate the performance of the line of sight correction platform. Results show that using the overdrive the -3 dB rejection frequency was increased from 1.1 Hz to 2.6 Hz. The suppression ability of the overdrive is about -20 dB at 0.1 Hz, however the normal-driving suppression ability is only about -13 dB.