In this paper, we study the effects of the occurrence of radial transport of particles in a tokamak on the efficiency of the current drive by lower hybrid (LH) waves, in the presence of an internal transport barrier. The results are obtained by numerical solution of the Fokker–Planck equation which rules the evolution of the electron distribution function. We assume that the radial transport of particles can be due to magnetic or electrostatic fluctuations. In both cases the efficiency of the current drive is shown to increase with the increase of the fluctuations that originate the transport. The dependence of the current drive efficiency on the depth and position of the barrier is also investigated.