The risk of subsynchronous resonance (SSR) is likely in power stations which are connected to power systems through series compensated transmission lines. Wind farms are not exempted from this issue. Recently a new technology of wind turbines, i.e. dual-rotor turbines, has been introduced. The performance of this wind turbine is enhanced compared to a single-rotor turbine in both aspects of energy efficiency and dynamic stability. However, since the number of mechanical components in dual rotor system is higher than the single-rotor case, therefore the risk of SSR in dual-rotor wind turbine is higher. This problem may be considered as a serious drawback for the new technology. This paper, at first, studies transient oscillations of the generator speed in both single and dual rotor systems after a sudden increase in electrical load. The frequency elements of the responses are calculated and compared together. Then, genetic algorithm (GA) is employed to optimize the dual-rotor system parameters for reducing the SSR possibility. This method assists us to lower the risk of SSR in dual-rotor wind turbine and keep it at the same level of single-rotor one.