A series of lead-free perovskite solid solutions of (1-x) Na0.5Bi0.5TiO3(NBT)x BaSnO3(BSN), for 0.0x0.15 have been synthesized using a high-temperature solid-state reaction route. The phase transition behaviors are studied using dielectric and Raman spectroscopic techniques. The ferroelectric to relaxor phase transition temperature (TFR) and the temperature corresponding to maximum dielectric permittivity (Tm) are estimated from the temperature-dependent dielectric data. Dielectric studies show diffuse phase transition around similar to 335 degrees C in pure NBT and this transition temperature decreases with increase in x. The disappearance of x-dependence of A1 mode frequency at similar to 134cm-1 for x0.1 is consistent with rhombohedral-orthorhombic transition. In situ temperature dependence Raman spectroscopic studies show disappearance and discontinuous changes in the phonon mode frequencies across rhombohedral (x<0.1)/orthorhombic (x0.1) to tetragonal transition