A technique for the instantaneous frequency measurement (IFM) of broadband signals is proposed based on stimulated Brillouin scattering (SBS) in a single-mode optical fiber. The instantaneous frequency and amplitude information is obtained by the narrowband filtering of the acoustic-optic interaction in the SBS process. Through sideband management of the optical-modulation, the IFM bandwidth can be far beyond the Brillouin frequency shift (i.e. ~11 GHz in 1550 nm). Proof-of-concept experiments for both the linearly frequency modulated pulse and frequency Costas coded pulse are carried out to verify the feasibility of the IFM.