Two noncentrosymmetric isostructural compounds Pb4Ga4GeQ12 (Q = S, Se) with their own structure type have been synthesized by solid-state reactions at high temperature. They crystallize in the tetragonal space group P42(1)c (No. 114) with a = 12.673(2) Å and c = 6.128(2) Å, and a = 13.064(7) Å and c = 6.310(5) Å, respectively, and Z = 2. The major structure motif features a three-dimensional framework constructed by chains of GaQ4 tetrahedra that are interconnected by separated GeQ4 tetrahedra at regular intervals. Interestingly, such a [Ga4GeQ12](8-) framework is flexible to allow the addition of Ag(+) or Li(+) to occupy the embedded A- or B-type of vacancies to generate the previously reported [AgGa5Q12](7-) or [LiGa5Q12](7-) interstitial compounds without symmetry breaking. The title compounds (Q = S, Se) have optical band gaps of 2.35 and 1.91 eV, respectively, and wide IR transparent regions of 0.80-22.5 and 0.75-22.5 μm, respectively. Significantly, the powder Pb4Ga4GeSe12 sample exhibits a strong second-harmonic-generation (SHG) response that is ∼2 times that of the benchmark AgGaS2 at a laser radiation of 2.05 μm with a non phase-matchable behavior. The calculated d36 coefficient agrees well with the experimental observation. The density functional theory (DFT) calculations suggest that the SHG response originates from the electronic transitions from Se 4p states to Pb 6p, Ga 4p, and Ge 4p states.