In this paper, dual-rotor counter-rotating (CR) configurations of vertical axis wind turbines (VAWTs) are briefly inspected and divided into three types. This investigation was focused on one of these types—the CR-VAWT with co-axial rotors, in which two equal rotors are placed on the same shaft, displaced from each other along it and rotated in opposite directions. For this CR-VAWT with three-blade H-Darrieus rotors, the properties of the design in terms of aerodynamics, mechanical transmission and electric generator, as well as control system, are analyzed. A new direct-driven dual-rotor permanent magnet synchronous generator was proposed, in which two built-in low-power PM electric machines have been added. They perform two functions—starting-up and overclocking of the rotors to the angular velocity at which the lifting force of the blades is generated, and stabilizing the CR-VAWT work as wind gusts act on the two rotors. Detailed in this paper is the evaluation of the aerodynamic performance of the CR-VAWT via 3D computational fluid dynamics simulations. The evaluation was conducted using the CONVERGE CFD software with the inclusion of the actuator line model for the rotor aerodynamics, which significantly reduces the computational effort. Obtained results show that both rotors, while they rotate in opposite directions, had a positive impact on each other. At the optimal distance between the rotors of 0.3 from a rotor height, the power coefficients of the upper and lower rotors in the CR-VAWT increased, respectively, by 5.5% and 13.3% simultaneously with some increase in their optimal tip-speed ratio compared to the single-rotor VAWT.