Rain-wind induced vibrations have been observed on numerous cable-stayed bridges around the world, which has resulted in an urgent need to gain further understanding of the phenomenon and to develop efficient means of mitigating the large-amplitude vibrations. It is believed that this aeroelastic instability problem is due to the formation and oscillation of a water rivulet on the upper cable surface, which changes the cable aerodynamics and absorbs energy into the system. In this paper, an analytical study of the phenomenon is conducted by formulating a finite element model for the cable and the upper rivulet with non-linear coupling effect. Linearization of the equations of motion of the cable-rivulet system is next carried out, based on which active vibration controller can be designed. Pole allocation control method has been employed for mitigating RWIV in the present study, which is able to add sufficient damping to several excited modes. The active controller is designed such that the closed-loop poles are allocated on the left half of the complex plane of eigenvalues. The controller gains obtained from the equivalent linear system are then applied to the original non-linear cable-rivulet system. Simulation results show that the proposed active modal controller performs much better in suppressing RWIV than an optimally tuned linear viscous damper.