Herein, we present a facile colloidal method to synthesize the high-quality AgGaS2 nanocrystals (NCs) within 2 min via exploiting the high-reactivity S precursor and then extend this synthetic strategy to the preparation of AgGaS2/ZnS core-shell NCs by a one-pot method without prior purification of AgGaS2 core. The as-synthesized samples were structurally characterized to confrim the formation of AgGaS2/ZnS core-shell NCs. The energy band gap of the AgGaS2/ZnS NCs can be effectively tunable from 2.98 to 2.83 eV by the control of their nonstoichiometry and further continuously decreases to 1.90 eV by the preparation of alloyed AgGaxIn1-xS2/ZnS NCs (1 <= x <= 0). Benefitting from the efficient band gap modulations, the photoluminescence (PL) colors of the AgGaS2-based NCs can cover almost the whole visible region from blue (460 nm) to red (671 nm). Our work demonstrates the one-pot synthesis of AgGaS2/ZnS core-shell NCs and their band gap engineering, which is of crucial in scalability toward industrial application and in tailoring optical characteristics of I-III-VI2 materials.