We calculate fluctuation Hall conductivity of a strongly type-II superconductor in strong electric fields by using the time dependent Ginzburg–Landau approach. Thermal fluctuations, represented by the Langevin white noise, are assumed to be strong enough to melt the Abrikosov vortex lattice created by the magnetic field into a moving vortex liquid. The layered structure of the superconductor is accounted for by means of the Lawrence–Doniach model. The nonlinear interaction term in dynamics is treated within self-consistent Gaussian approximation and we go beyond the often used lowest Landau level approximation to treat arbitrary magnetic fields. The results are compared to experimental data on high-T c superconductor YBa2Cu3O7−δ .