In this paper, we consider analysis and processing of chirp pulses using the matched fractional Fourier transform (FRFT). Using the properties of the FRFT and the ambiguity function, the resolution performances of time delay and Doppler shift for chirp pulses based on the matched FRFT are derived systematically. The method for sidelobe suppression using the matched FRFT is also proposed. Simulation results are presented for testifying the theoretical derivations.