A mathematical model describing the concentration polarization in the three-phase contact region during the Langmuir-Blodgett deposition process is developed. It is shown that the stationary deposition is only possible when, in additional to convective fluxes, electrodiffusion ionic fluxes and corresponding concentration gradients are developed in the system. At a sufficiently low withdrawal speed, the occurring diffusion and migration ionic fluxes restore the steady-state ionic balance. As well, electric charge is accumulated in close vicinity to the three-phase contact line to produce a stationary electric field. The concentration polarization affects the parameters of the deposition process (dynamic contact angle, work of adhesion, maximum deposition rate) as well as morphology, composition, and structure of the deposited monolayer. When the withdrawal speed exceeds a critical value, the transport of counterions becomes insufficient to compensate interfacial charge in close vicinity to the three-phase contact line. Consequently, the electrostatic repulsion between the monolayers becomes sufficiently strong to disrupt the deposition process. The latter can result in meniscus instability. The proposed mechanism correlates with some experimental observations.