Tungsten bronze structure $Sr_{1-x}Ba_xNb_2O_6$ (SBN) single crystals were grown primarily using the Czochralski method, in which several difficulties were encountered: striation formation and diameter control. Striation formation occurred mainly because of crystal rotation in an asymmetric thermal field and unsteady melt convection driven by thermal buoyancy forces. To optimize the growth conditions, bulk SBN crystals were grown in a furnace with resistance heating elements. The zone of $O_2$ atmosphere for crystal growth is 9.0 cm and the difference of temperature between the melt and the top is $70^{circ}C$. According to the growth conditions of the rotation rate, grown SBN became either polycrystalline or composed of single crystals. In the case of as-grown $Sr_{1-x}Ba_xNb_2O_6$ (x = 0.4; 60SBN) single crystals, the color of the crystals was transparent yellowish and the growth axis was the c-axis. The facets of the crystals were of various shapes. The length and diameter of the single crystals was 50~70 mm and 5~10 mm, respectively. Tungsten bronze SBN growth is affected by the temperature profile and the atmosphere of the growing zone. The thermal expansion coefficients on heating and on cooling of the grown SBN single crystals were not matched. These coefficients were thought to influence the phase transition phenomena of SBN.