Inertia control system for a wind turbine comprising a rotor (5), generator (12) driven by the rotor (5) that interacts with a power converter (13) to generate electricity, a wind turbine controller (15) that comprises a blade pitch controller (19) and a generated power controller (18), a controller for the power converter (14) that interacts with the wind turbine controller (15), characterized because it comprises an inertia emulation block (17) that generates an extra power signal (32) negatively proportional to the frequency change rate (23) that is added to the power reference of the wind turbine generated power controller (15) and adapts the rotational speed reference of the wind turbine controller (15) according to the grid frequency (21) to prevent distortion in the active power output after adding or subtracting power in proportion to the frequency change rate (23).