Self-starting characteristics is a challenging issue in the field of Darrieus-type vertical axis wind turbines. Traditionally, the numerical simulations were performed at several constant rotational velocities for the turbine and the generated torques were reported for each rotational velocity, neglecting the effects of the turbine inertia on the transient start-up motion of the turbine. In the current study, a numerical method is proposed to study the self-starting characteristics of a Darrieus wind turbine, considering the turbine moment of inertia. The simulation starts from the initial stationary state and continues until the final steady-periodic condition. At each time step, the instantaneous rotational velocity of the turbine is computed based on the Newton's second law, according to the instantaneous aerodynamic and mechanical forces acting on the turbine. Results indicate that as the rotor inertia increases, it takes a longer time for the turbine to reach its final velocity, in a manner that, the turbine might even fail to reach the final condition and the rotation halts. Results also show that as the rotor inertia decreases, the oscillations amplitude of the turbine rotational velocity increases. This can enable the turbine to pass higher resistant torques than those computed based on the traditional method. (C) 2017 Elsevier Ltd. All rights reserved.