The linear electro-optic (EO) effect of near-infrared femtosecond laser pulses with high intensity in MgOLiNbO3 crystal is numerically investigated. It is found that, if an external electric field is applied along the direction perpendicular to the optical axis of crystal and is set at the optimization value of EO effect, a high input intensity will result in the broadening of output pulses in normal dispersion region. And in abnormal dispersion region, the output durations become narrower when the input light intensity becomes higher. For the light pulse with central wavelength at λ0=1.6335 μm, the output durations can be compressed by this EO effect. For example, with the input pulse duration T0=5 fs and intensity I0=20 GW/cm2 fixed, the minimum output duration is 0.76 T0. And for T0>5 fs, the minimum output duration is less than 0.76 T0. If another external electric field is applied along the direction of optical axis of crystal to modulate the phase of light pulse，the central wavelength corresponding to the minimum pulse duration will make a blue or red shift and the shift becomes large with the increase of applied electric field.