In this paper, the gas-liquid two-phase flow in a multi-stage transonic compressor is numerically simulated based on the Euler-Lagrange method. The changes in wet compression aerodynamic characteristics of the compressor are investigated under various spraying conditions (droplets sizes and spraying rates). The results indicate that the compressor choking boundary moves to a smaller flow rate after spraying. Wet compression improves efficiency of the compressor. The evaporation cooling effect of wet compression decreases the total temperature ratio and augments the specific power, resulting in an enhanced total pressure ratio. After the water droplets are injected into the compressor, due to the small rise of the airflow temperature in the upstream aera, the evaporation cooling effect of droplets is weak. Negative effects of droplets lead to a reduction in total pressure ratio of the first-stage compressor. As water droplets move downstream, the gradual increase in airflow temperature enhances the evaporation cooling effect, thereby improving the compressor performance. Water droplets migrate radially inside the compressor and gather toward the blade tip area, causing the gas phase mass flow inside the compressor to be redistributed in the radial direction. Wet compression enhances the capability of the rotor blades to perform work an airflow, leading to an increase in the airflow twist velocity.