Discrete modulation continuous variable measurement device independent quantum key distribution scheme has good compatibility with efficient error correction codes, which leads to high reconciliation efficiency even at low signal-to-noise ratio. Besides, the implementation of this protocol is simpler than that of Gaussian modulation scheme. However, the quantum efficiency of homodyne detector commonly used in the experiment is only 0.6, which will seriously affect the practical application performance of discrete modulation continuous variable measurement device independent quantum key distribution scheme. To solve this problem, we propose a discrete modulation continuous variable measurement device independent quantum key distribution scheme based on realistic detector compensation. In our scheme, for the outputs of two quantum channels, each adopts a phase sensitive amplifier to compensate for the corresponding realistic homodyne detector. The simulation results show that the phase sensitive amplifier can well compensate for the quantum efficiency of the realistic detector and effectively improve the performance of the discrete modulation continuous variable measurement device independent quantum key distribution scheme with realistic detector in terms of secret key rate and secure transmission distance. The proposed protocol provides an effective method for promoting the practical development of the discrete modulation continuous variable measurement device independent quantum key distribution scheme.