We report the synthesis of $SrTiO_3$, $BaTiO_3$ and $Ba_xSr_{1-x}TiO_3$ (BST) nanoparticles (NPs) in various compositions (x = 0.25, 0.5 and 0.75) by an inorganic sol-gel method under a basic condition. Highly crystalline nanoparticles were formed at the reaction temperature of 25 - $100^{circ}C$ from a stabilized titanium alkoxide in tetramethylammonium hydroxide (TMAH) and barium or strontium acetate in aqueous solution. Morphology and particle structure of the synthesized BST NPs were characterized by scanning electron microscopy (SEM), X-ray diffraction (XRD) and transmission electron microscopy (TEM). The BST nanoparticles in various compositions were monodispersed without mutual aggregation, and their average sizes were in the range of 70 - 80 nm. Furthermore, they showed highly crystallized perovskite phase over the whole composition range from $SrTiO_3$ to $BaTiO_3$. We also proposed a mechanism for the low-temperature formation of BST NPs.