Penetration of grid connected inverters (GCI) has arisen in power systems due to increasing integration of renewable sources. However, restrictive grid codes require that renewable sources connected to the grid with power electronic systems must be properly connected and appropriate currents must be injected to support stability of the grid under grid faults. Simultaneous injection of symmetrical positive and negative sequence currents is mandatory to support stabilization of grid at the instant of grid faults. Conventional synchronously rotating frame dq current controllers are insufficient under grid faults due to low bandwidth of PI controllers. This paper proposes a new grid current control strategy for grid connected voltage source inverters under unbalanced grid voltage conditions. A proportional current controller with a first order low pass filter disturbance observer (DOb) is proposed which establishes positive sequence power requirements and independently control negative sequence current components under unbalanced voltage conditions. The method does not need any parameter, since it estimates nonlinear terms with low pass filter DOb. Simulations are implemented in Matlab/Simulink platform demonstrating the effectiveness of proposed method.