A novel method for simultaneous measurement of temperature, refractive index (RI), and axial strain based on the forward Brillouin scattering (FBS) in double-coated single-mode fiber (SMF) with polyimide outer coating is proposed. The changes in temperature, RI, and axial strain all change the acoustic properties of polyimide coating fiber and show different responses to transverse acoustic waves. The new phenomena are that frequency shifts and linewidths of FBS in polyimide coating optical fiber corresponding to different radial acoustic modes have linear relationships with temperature, RI, and axial strain. By monitoring the three parameters of frequency shifts and/or linewidths of FBS corresponding to different radial acoustic modes, the temperature, RI, and axial strain changes can be obtained. In a proof-of-concept experiment, the frequency shifts of FBS spectra of two radial acoustic modes and the linewidth of FBS spectrum of one radial acoustic mode linearly depend on the temperature, RI, and axial strain, which have different response coefficients of frequency shift-temperature, linewidth-temperature, frequency shift-RI, linewidth-RI, frequency shift-axial strain, and linewidth-axial strain. Based on these linear relationships, the simultaneous measurement of temperature, RI, and axial strain is achieved experimentally in polyimide-coated SMF. The experimental results show that the measurement uncertainties of temperature, RI, and axial strain are 0.1 degrees C, 0.0003, and 10.5 mu epsilon, respectively. In addition to having high precision, such a fiber sensor has the advantages of simplicity, stability, and persistence, which has great potential applications in many sensing fields, such as biochemical sensing, marine environment, and marine structural health monitoring.