  We investigate a higher-group structure of massless axion electrodynamics in
$(3+1)$ dimensions. By using the background gauging method, we show that the
higher-form symmetries necessarily have a global semistrict 3-group (2-crossed
module) structure, and exhibit 't Hooft anomalies of the 3-group. In
particular, we find a cubic mixed 't Hooft anomaly between 0-form and 1-form
symmetries, which is specific to the higher-group structure.
