A method using chirp-matching optical parametric chirped pulse amplification (OPCPA) scheme to improve the signal-to-noise ratio (SNR) of ultrashort laser pulse is proposed. Comparing the chirp-matching OPCPA scheme with the usual OPCPA scheme, it is shown that the chirp-matching OPCPA scheme can improve significantly the SNR of ultrashort laser pulse, and obtain high conversion efficiency simultaneously. The method for determining the chirp parameter which satisfies the chirp-matching condition is presented. The effects of the crystal length, the noise bandwidth, the pump chirp, as well as the synchronization of signal and pump pulses on the improvement of SNR are also analyzed by numerical simulation.