A new lead-free perovskite solid solution of (1-x)BaTiO3–xBiAlO3 (x=0.02, 0.05, 0.10, and 0.15) that exhibits ferroelectric properties and relaxor behavior has been synthesized by solid state reactions. X-ray diffraction patterns show a transformation from the tetragonal symmetry into a rhombohedral symmetry as a result of the substitutions of Bi3+ on the A site and Al3+ on the B site in the crystal lattice of BaTiO3. The temperature and frequency dependences of the dielectric constant indicate a crossover from a normal ferroelectric to relaxor behavior. The degree of deviation from the Curie–Weiss law is found to increase with the increasing amount of BiAlO3. The high-temperature slope of the dielectric peak for x=0.05, 0.1 and, 0.15 can be well described by a Lorenz-type relation. Typical relaxor behavior is observed for x=0.15 with the temperature of the dielectric peak Tm=360 K at 1 kHz, while ferroelectric hysteresis loop is displayed at room temperature. This suggests that the long-range polar order from the end member BaTiO3 persists and coexists with polar nanoregions induced by the chemical disorder following the coupled substitutions in the solid solution.