Recently developed chalcogenides nonlinear optical crystals have potential application in mid- to far infrared laser fields. However, high-quality single crystals are hard to be prepared because of high vapor pressure of sulfur component and decomposition of chalcogenides during the polycrystalline synthesis and single-crystal growth. A pressure assisted technique was performed to prepare stoichiometric AgGaS2 and AgGaGeS4 polycrystalline materials. On the basis of the synthesized polycrystalline materials, high-quality AgGaS2 and AgGaGeS4 single crystals were successfully obtained using the seed directional Bridgman method with a well-designed crucible-capsule technique. These single crystals possess high homogeneity and low absorption coefficient, making it can be applied in nonlinear optical experiments. The pressure-assisted method can also be suitable to prepare other chalcogenide and phosphide compounds. The method of polycrystalline synthesis and single crystals growth described in this work will be helpful for preparing other chalcogenides nonlinear optical crystals.