Single crystals in the (Na1/2Bi1/2)TiO3-CaTiO3 system have been grown for the first time using the solid state crystal growth method. Seed crystals of SrTiO3 were buried in 0.96(Na1/2Bi1/2)TiO3-0.04CaTiO3 (NBT-4CT) powder which was then pressed into pellets. Pellets were sintered and single crystals of NBT-4CT grew on the seeds. Electron probe micro analysis shows that the chemical composition of the single crystal is close to the nominal composition. X-ray diffraction and micro-Raman scattering analysis shows that the single crystal has the rhombohedral (Na1/2Bi1/2)TiO3 structure. Single crystals were also grown by bonding a seed crystal to a pre-sintered NBT-4CT pellet and annealing. The single crystal shows dielectric behavior similar to that of NBT-4CT ceramics and other (Na1/2Bi1/2)TiO3 -based ceramics and single crystals. Characteristic dielectric transitions can be related to the rhombohedral-tetragonal and tetragonal-cubic phase transitions. The NBT-4CT single crystal has improved ferroelectric and piezoelectric properties compared to the bulk polycrystalline ceramic.