(1 − x)(Bi1/2Na1/2)TiO3 − xBaTiO3 has been the most studied Pb-free piezoelectric material in the last decade; however, puzzles still remain about its phase transitions, especially around the important morphotropic phase boundary (MPB). By introducing the strain glass transition concept from the ferroelastic field, it was found that the phase transition from tetragonal (T, P4bm) to rhombohedral (R, R3c) was affected by a strain glass transition at higher temperature for x ≥ 4%. In these compositions, the T–R transition was delayed or even totally suppressed and displayed huge thermal hysteresis upon cooling and heating. Also, isothermal phase transitions were predicted and realized successfully in the crossover region, where the interaction between the T–R transition and the strain glass transition was strong. Our results revealed the strain glass nature in compositions around the MPB in this important material, and also provide new clues for understanding the transition complexity in other (Bi1/2Na1/2)TiO3-based Pb-free piezoelectric materials.