AgGaGenS2(n+1) crystal is a series of quaternary nonlinear optical materials for mid-IR laser applications of converting a 1.064 mu m pump signal (Nd:YAG laser) to 4-11 mu m laser output, but only AgGaGeS4 has attracted the most attention, remaining the other promising AgGaGenS2(n+1) crystal whose physicochemical properties can be modulated by n value. In this work, AgGaGenS2(n+1) (n = 2, 3, 4, and 5) polycrystals are synthesized by vapor transport and mechanical oscillation method with different cooling processes. High-resolution X-ray diffraction analysis and refinement have revealed that all the four compounds are crystallized in the noncentrosymmetric orthorhombic space group Fdd2, resulting in the excellent nonlinear optical property, and the distortion of tetrahedron with the variation of n value causes the discrepancy of physicochemical property. Besides, using the modified Bridgman method, AgGaGenS2(n+1) single crystals with 15 mm diameter and 20-40 mm length have been grown. We have discussed the structure and composition of AgGaGenS2(n+1) by XPS spectra and analyzed the three kinds of vibration modes of tetrahedral clusters by the Raman spectra. The Hall measurement indicates that the AgGaGenS2(n+1) single crystals are p-type semiconductor, and the carrier concentration decreases with the increasing n value. All the transmittances of as-grown AgGaGenS2(n+1) samples exceeds 60% in the transparent range, especially the transmittance of AgGaGe2S6, is up to 70% at 1064 nm, and the band gap of as-grown crystal increases from 2.85 eV for AgGaGe2S6 to 2.92 eV for AgGaGe5S12. After a thermal annealing treatment, the absorptions at 2.9, 4, and 10 mu m have been eliminated, and the band gap changed into the range of 2.89-2.96 eV.