We have analyzed the characteristic features and problems in the major approaches to measurement of laser frequency noise. We propose a method in which we use an unbalanced fiber-optic interferometer, generation at the optical system output of a signal for a subcarrier of the frequency, phase-modulated by fluctuations in the laser frequency, and measurement of the spectrum for this signal. The proposed approach is distinguished by relative simplicity and accessibility, and does not require using uncommon specialized instruments and complicated specific procedures.