Near-stoichiometric lithium niobate (SLN) crystals doped with low iron are grown, in which the mass fractions of iron are 0×10-6, 5×10-6, 10×10-6, 25×10-6, 50×10-6, 100×10-6, respectively. And their ultraviolet-visible transmission spectra are measured. The concentrations of Fe2+ and Fe3+ are estimated by the linear absorption coefficients at the wavelength of 477 nm. The dynamic process and steady characteristics of the light-induced absorption of crystals are investigated by the pump-probe (365 nm and 632.8 nm) method. The results show that the dark decay process of light-induced absorption exhibits a stretched-exponential behavior, and the decay time constant (i.e., the small polaron lifetime) decreases with the Fe-doped concentration and the pump intensity, while the stretching factor decreases with the pumping intensity. The electron transport equations are solved numerically by the four-order Runge-Kutta method, and the whole process of the light-induced absorption in the SLN crystals doped with Fe is simulated, which is consistent with the experimental results.