The first lead tellurate-nitrate nonlinear-optical (NLO) crystal, Pb9Te2O13(OH)(NO3)(3), featuring a 3D anionic diamondlike toplogical structural motif formulated as [Pb9O13](8-) constructed by unique nonanuclear basket-shaped Pb@Pb8O14 clusters has been hydrothermally achieved, in which the Pb@Pb8O14 cluster shows a core-shell structure with one PbO10 polyhedron enclosed by eight PbOx (x = 3 and 4) polyhedera via edge and face sharing. The hexavalent Te in TeO5(OH) octahedra is linked to a [Pb9O13](8-) cluster to form a rare [Pb9Te2O13(OH)](3+) cationic framework. The compound demonstrates a powder second-harmonic-generation (SHG) response of about 1.2 times that of KH2PO4 (KDP) as well as a wide transparency range. Calculations on the local dipole moment and SHG coefficient reveal that the net polarization is zero because of a Kleinman-forbidden point group. Further analysis shows that the SHG response results from structure-induced variations by thermal vibrations of the lattice rather than the intrinsic dipole moment, which offers another insight on the design of new NLO materials.