  We compute the electrical conductivity of quark-gluon plasma in a strong
magnetic field $B$ with quantum field theory at finite temperature using the
lowest Landau level approximation. We provide the one-loop result arising from
1-to-2 scattering processes whose kinematics are satisfied by the (1+1)
dimensional fermion dispersion relation. Due to the chirality conservation, the
conductivity diverges in the massless limit, and is sensitive to the value of
the current quark mass. As a result, we find that the conductivity along the
direction of the magnetic field is quite large compared with the value at
$B=0$, mainly because of the small value of the current quark mass. We show
that the resummation of the ladder diagrams for the current-current correlator
gives rise to only sub-leading contributions beyond the leading-log order, and
thus verify our one-loop result at the leading-log accuracy. We also discuss
possible implications for the relativistic heavy-ion collisions.
