Cesium lead halide perovskite quantum dots (QDs) have recently emerged as highly promising opto-electronic materials. Despite the relative facile anion exchange reactions in cesium lead halide perovskite QDs, in depth study of the anion exchange reactions such as reaction kinetics are required that can provide insight into the crystal transformation in the cesium lead halide perovskite QDs. Herein, we investigated the anion exchange reaction from CsPbI3 QDs to CsPbBr3 QDs with varying the particle size of the starting CsPbI3 QDs. By characterizing the PL spectra in the anion exchange reaction process, we observed that discontinuous PL peak shifts during I-to-Br anion exchange reaction in starting CsPbI3 QDs over a critical size. Origin of the discontinuous I-to-Br anion exchange kinetics are mainly due to thermodynamically unstable nature of the CsPb(Br/I)3 alloy QDs.