Electro-optic sampling (EOS) is often used to detect electric field waveform in the time domain of wideband terahertz radiation, and then it is also used to detect few-cycle laser pulse electric field waveform in the near-infrared to mid-infrared band. In this technique, the performance of electro-optic crystal directly affects its detection performance and frequency response bandwidth. In this paper, the frequency response characteristics and bandwidth of EOS based on lithium niobate crystal in the near-infrared band are studied, and the application of this technology in detecting few-cycle laser pulses is analyzed in detail, especially the distortion of few-cycle laser pulses caused by the detection process (including the changes of its center frequency and bandwidth). It is found that in the near-infrared band of 900--2500 nm, the measurement error of the few-cycle pulse with 1.5 oscillation cycles depends on the crystal thickness and the laser wavelength to be measured. When the crystal thickness is 10 μm, the deviation between bandwidth and center frequency is less than 1%. When the crystal thickness is 100 μm, the resulting maximum deviation of bandwidth is 25% and the maximum deviation of center frequency is 10%. For the few-cycle pulse with 2.5 oscillation cycles, the deviation of bandwidth and center frequency is obviously reduced. This paper provides a good theoretical reference for measuring the electric field waveform of few-cycle laser pulses in near-infrared band by means of EOS crystal.