The electrical conductivity of plasma in a strong spatially inhomogeneous magnetic field has been calculated using the small-gyroradius approximation to the kinetic equation. The current which flows along the magnetic lines is the sum of two parts, one due to the time-independent applied electric field, and the other (secondary currents) associated with gradient-B drifts across the lines. The first part gives the electrical conductivity. It has a non-local dependence on the electric field, when the mean free path is not short compared with the scale length for magnetic variations along the field lines. The kinetic equation is solved by a perturbation technique in the long-mean-free-path limit, and an explicit expression for the conductivity is obtained. The main result is that the inhomogeneity reduces the conductivity approximately by the fraction of trapped particles.