Hefei Infrared Free Electron Laser (IR-FEL) is a free electron laser device operating in mid-infrared and far-infrared. To achieve its design targets, a low level radio frequency (LLRF) system is needed to monitor and control the amplitude and phase of the acceleration field in the accelerator cavity. However, the input-to-output nonlinear characteristic of the amplitude of the klystron decreases the control gain near the saturated region, which reduces the efficiency of feedback. In this paper, a predistortion algorithm based on FPGA is designed to correct the nonlinear characteristics of the amplitude of the klystron, and the 2048-node direct lookup-table algorithm and the 32-node lookup-table with linear interpolation algorithm are compared and tested online. The comparison shows that, in the condition of accuracy requirement, the direct lookup-table algorithm consumes 25% less clocks than the lookup-table with linear interpolation algorithm, with less total resource consumption. The feedback efficiency is compared on Toshiba E3729 klystron, and it is improved by 43% after adding the direct lookup-table algorithm based predistortion module.