Single crystals of K6Cd3(C3N3O3)(4) (1) were successfully grown via a solid-state cyclotrimerization reaction method from Cdl(2) and KOCN. To our best knowledge, it is the first inorganic compound containing isolated six-membered-ring (6-MR) anionic groups that crystallizes in the cubic system. In the structure, the basic 6-MR anionic unit is a planar pi-conjugated (C3N3O3)(3-) group that is isoelectronic with the (B3O6)(3-) group, as Observed in the benchmark nonlinear-optical (NLO) crystal beta-BaB2O4 with strong second-harmonic-generation response. In addition, the electronic structure and linear optical and NLO properties for 1 were also investigated by the first-principles calculation. The NLO coefficient (d(14) = 1.17 pm/V) of 1 is about 3 times that of KH2PO4.