We demonstrate an arbitrary-response Brillouin instantaneous frequency measurement (IFM) based on the principle of the frequency-to-power mapping in stimulated Brillouin scattering (SBS), which is named Brillouin IFM. The arbitrary response is realized by periodically sweeping the frequency of the local pump lightwave, and the response's amplitude depends on the sweeping slope. The Brillouin IFM is achieved by the control of the sweeping period lower than the double of the flight-of-time in the SBS interaction length. A Costas frequency coded pulse is experimentally measured to verify the feasibility of the proposed Brillouin IFM scheme. The bandwidth of the digital sampling in the scheme is reduced to 50 MHz. The Brillouin IFM range without averaging reaches 6 GHz at Ku band.