The exploration of novel infrared nonlinear optical (IR NLO) materials with large second-harmonic generation (SHG) responses and wide band gaps has become very imperative recently. Herein we reported two noncentrosymmetric compounds, LiBa(4)Ga(2)Q(2) (Q= S, Se), crystallizing in space group P (4) over bar2(1)c (No. 114), which feature 3D frameworks built by a basic [Ga(5)Q(16)](17-) windmill cluster and LiQ(4) tetrahedra in a cesium chloride topological structure. Both compounds satisfy the desired balance between good SHG responses (similar to 1.5X that of AgGaS2) and wide band gaps (3.43 and 2.44 eV) with remarkable laser damage thresholds (21X and 6x that of AgGaS2). The theoretical calculations uncover that the [Ga(5)Q(16)](17-) cluster makes major contributions to the SHG effect in LiBa(4)Ga(5)Q(2). In addition, the structure-performance relationship among all compounds in the I-II4-III5-VI12 system has been discussed systematically, which indicates that the introduction of the alkali metal lithium in the I site is beneficial for the production of large band gaps. This work will be helpful in exploring novel IR NLO materials with special structures and comprehensive properties in the chalcogenide system.