This paper presents a current controller for a transformerless single-phase two-level inverter grid connected by means of an LCL output filter and subject to a sever harmonic distortion in the grid voltage signal. The controller indirectly controls the grid-side current by controlling the inverter-side current. The inverter-side current controller is simpler to implement, moreover, it is shown that a damping injection can be done by a simple proportional action of the measured current. Instrumental for the proposed scheme is the proper design of the inverter-side current reference, which must guarantee that the grid-side current reaches its corresponding reference, i.e., a pure sinusoidal signal with the appropriate phase-shift. It is shown that the inverter-side current has to be distorted as much as necessary to guarantee that the grid-side current reaches its reference. The controller includes a harmonic compensation mechanism, therefore, it is aimed to properly perform under harmonic distortion operation. Numerical tests are presented to assess the performance of the proposed scheme. Experiments are under development and will be presented in the final version of the paper.