A numerical method for modelling the aerodynamic interaction between rotor blades and an independently generated vortex is developed. In this method, the Navier—Stokes/Euler equations are adopted for capturing the features of rotor blade—vortex interaction (BVI) flow and the overset grids technique is used for multi-zone solution. To incorporate the effects of the vortex in the solution, a generalized grid-velocity approach is presented to simplify the computations. The acoustic prediction is based on the well-known Ffowcs Williams-Hawkings (FW-H) equation for acoustic pressure. By this method developed, a parametric study is performed to examine the effects of the vortex strength, miss-distance, core-radius, oblique interaction, and interaction angle in a blade-shaft plane on BVI noise. The results indicate that the increase in miss-distance, core-radius, obliqueness of interaction, or interaction angle in a blade-shaft plane is an effective approach to reduce BVI noise, makes the BVI noise less impulsive (lower high harmonic content in noise energy) and increases the high noise encompassed area. However, the decrease in vortex strength changes only the magnitude of noise, not its distribution in different harmonics. The research also indicates that oblique interaction in a rotor plane has a significant effect on radiation directionality, while other parameters show little impact on it.