Phase-sensitive amplification is of great research interest owing to its potential in noiseless amplification. One key feature in a phase-sensitive amplifier is the gain extinction ratio defined as the ratio of the maximum to the minimum gains. It quantifies the capability of the amplifier in performing low-noise amplification for high phase-sensitive gain. Considering a phase-sensitive fibre optical parametric amplifier for linear amplification, the gain extinction ratio increases with the phase-insensitive parametric gain achieved from the same pump. In this work, we use backward Raman amplification to increase the phase-insensitive parametric gain, which in turn improves the phase-sensitive operation. Using a 955 mW Raman pump, the gain extinction ratio is increased by 9.2 dB. The improvement in the maximum phase-sensitive gain is 18.7 dB. This scheme can significantly boost the performance of phase-sensitive amplification in a spectral range where the parametric pump is not sufficiently strong but broadband Raman amplification is available.