In this article, we report the evolution of the dielectric behavior from a dielectric relaxor to a ferroelectric relaxor with variation of Bi concentration in (Sr1−1.5xBix)TiO3 (0⩽x⩽0.2). In the doping range 0.0005⩽x⩽0.002, two dielectric modes A and B are induced. The temperature (Tm) where the permittivity maximum occurs for modes A and B is independent of Bi concentration and of dc electric fields. The complex permittivity of modes A and B follows the empirical Cole–Cole equation. The relaxation time for modes A and B follows the Arrhenius law. The dielectric possessing this type of dielectric behavior is named as a “dielectric relaxor.” At x⩾0.0033, an additional mode C appears, whose Tm increases with increasing Bi concentration. The complex permittivity for mode C does not follow the Cole–Cole equation. The relaxation time of mode C follows the Vogel–Fulcher law, indicating typical relaxor-ferroelectric behavior. In this work, we refer it to a “ferroelectric relaxor” mode. In the range of 0.0033⩽x⩽0.133, the coexistence of the dielectric-relaxor modes and the ferroelectric-relaxor mode is observed. In the samples doped with higher Bi concentration, modes A and B gradually merge into mode C, and only ferroelectric-relaxor behavior remains at x⩾0.133. This system provides a composition-controlled example of evolution from a “dielectric relaxor” to a “ferroelectric relaxor.” In addition, some controversial interpretations of the dielectric behavior of the Bi doped SrTiO3 solid solutions in the literature are discussed, and the polarization relaxation species of modes A and B are attributed to Bi ions.