We report on the low-frequency current fluctuations and electronic noise in thin-films made of Bi(2)Se(3) topological insulators. The films were prepared via the "graphene-like" mechanical exfoliation and used as the current conducting channels in the four- and two-contact devices. The thickness of the films ranged from ∼50 to 170 nm to avoid hybridization of the top and bottom electron surface states. Analysis of the resistance dependence on the film thickness indicates that the surface contribution to conductance is dominant in our samples. It was established that the current fluctuations have the noise spectrum close to the pure 1/f in the frequency range from 1 Hz to 10 kHz (f is the frequency). The relative noise amplitude S(I)/I(2) for the examined Bi(2)Se(3) films was increasing from ∼5 × 10(-8) to 5 × 10(-6) (1/Hz) as the resistance of the channels varied from ∼10(3) to 10(5) Ω. The obtained noise data is important for understanding electron transport through the surface and volume of topological insulators, and proposed applications of this class of materials. The results may help to develop a new method of noise reduction in electronic devices via the "scattering immune" transport through the surface states.