The exploration of new infrared (IR) nonlinear optical (NLO) crystals with large second-harmonic generation (SHG) responses and high laser-induced damage thresholds (LIDTs) concurrently is urgently needed and challenging. Herein, the first-type of noncentrosymmetric (NCS) alkali metal Ag-based thiophosphates KAg₂PS₄ (1) and (Na_0.30K_0.70)Ag₂PS₄ (2) were successfully synthesized using a high-temperature solid-state method. In their structures, AgS₄ tetrahedra are interconnected by sharing corner S atoms to construct {[AgS₄]⁷⁻}_∞ layers, which are linked with isolated PS₄ tetrahedra to build three-dimensional open tunnel structures, providing cavities occupied by K or Na/K atoms. Both 1 and 2 exhibit phase-matchable large SHG effects about 1.40 and 1.65 times that of AGS. Moreover, they possess wide band gaps of 2.92 and 2.89 eV, and exhibit high LIDTs of 3.19 and 2.77 × AGS, respectively. Theoretical calculation results confirm that the highly distorted AgS₄ tetrahedra contribute a lot to their NLO responses. This work indicates that 1 and 2 can serve as high-performance IR NLO materials. More importantly, a new class of promising IR NLO materials (alkali metal Ag-based thiophosphates) will shed useful light on future exploration.