  We formulate a notion of the quantum automorphism groups of $2$-graphs. We
show that two isomorphic $2$-graphs have isomorphic quantum automorphism groups
making the notion well-defined. We compute the quantum automorphism groups of a
few $2$-graphs. It is observed that quantum automorphism group of a $1$-graph
can be realized as the quantum automorphism group of a $2$-graph.
