  We study higher-form symmetries in a low-energy effective theory of a
massless axion coupled with a photon in $(3+1)$ dimensions. It is shown that
the higher-form symmetries of this system are accompanied by a semistrict
3-group (2-crossed module) structure, which can be found by the correlation
functions of symmetry generators of the higher-form symmetries. We argue that
the Witten effect and anomalous Hall effect in the axion electrodynamics can be
described in terms of 3-group transformations.
