While electronic states with nontrivial topology have traditionally been known in insulators, they have been evidenced in metals during the past 2 years. Such Weyl semimetals show topological protection while conducting electricity both in the bulk and on the surface. An outstanding question is whether topological protection can happen in metals with strong correlations. Here, we report theoretical work on a strongly correlated lattice model to demonstrate the emergence of a Weyl–Kondo semimetal. We identify Weyl fermions in the bulk and Fermi arcs on the surface, both of which are associated with the many-body phenomenon called the Kondo effect. We determine a key signature of this Weyl–Kondo semimetal, which is realized in a recently discovered heavy-fermion compound.