We report results of investigation of the low-frequency excess noise in device channels made from topological insulators – a new class of materials with a bulk insulating gap and conducting surface states. The thin-film Bi2Se3 samples were prepared by the ‘graphene-like’ mechanical exfoliation from bulk crystals. The fabricated four-contact devices had linear current–voltage characteristics in the low-bias regime |VSD| < 0.1 V. The current fluctuations had the noise spectral density SI ∼1/f for the frequency f < 10 kHz. The noise density SI followed the quadratic dependence on the drain–source current and changed from about ∼10−22 to 10−18 A2/Hz as the current increases from ∼10−7 to 10−5 A. The obtained data is important for planning transport experiments with topological insulators. We suggest that achieving the pure topological insulator phase with the current conduction through the ‘protected’ surface states can lead to noise reduction via suppression of certain scattering mechanisms. The latter has important implications for implementing the ultra-low-power and ultra-low-noise electronics.