We propose a unique multi-parameter optical fiber sensor based on intramodal stimulated Brillouin scattering of higher-order acoustic modes in inverse-parabolic graded-index fiber (IPGIF) without a mode converter. Both optical modes and acoustic modes guided in the IPGIF are characterized and demonstrated theoretically and experimentally. Simulation analysis shows that the multi-peak feature in the Brillouin gain spectrum of the IPGIF is attributed to the couplings between the guided optical mode and the higher-order acoustic modes. Thanks to the distinct acoustic properties of the peaks induced by the sharp refractive index profile of the IPGIF, the different temperature and strain dependences of the first three Brillouin peaks enable the discrimination of the temperature and strain at an accuracy of 0.85°C and 17.4 με.