In the present paper we compute the Jacobian group of $Δ$-graph $Δ(n; k, l, m).$ The notion of $Δ$-graph continues the list of families of $I$-, $Y$- and $H$-graphs well-known in the graph theory. In particular, graph $Δ(n; 1, 1, 1)$ is isomorphic to discrete torus $C_3\times C_n.$ It this case, the structure of the Jacobian group will be find explicitly.