The practical applications of CsPbX3 nanocrystals (NCs) have been limited by their poor stability. Although much effort has been devoted to making core-shell nanostructures to enhance the stability of CsPbX3 NCs, it is still very difficult to coat CsPbX3 NCs with another material on a single-particle level. In this work, we report a facile one-pot approach to synthesize CsPbBr3@SiO2 core-shell nanoparticles (NPs), in which each core-shell NP has only one CsPbBr3 NC. The formation process has been carefully monitored. It has been found that the formation rates, determined by reaction temperature, precursor species, pH value, etc., of both CsPbBr3 and SiO2 are critical for the successful preparation of core-shell NPs. Thanks to the protection of SiO2 shell, the product shows much higher long-term stability in humid air and enhanced stability against ultrasonication treatment in water than that of naked CsPbBr3 NCs. This work not only provides a robust method for the preparation of core-shell nanostructures but also sheds some light on the stabilization and applications of CsPbX3 NCs.