New interconnection standards for Photovoltaic systems are going to be mandatory in some countries. Such that the next generation of PV should support a full range of operation mode like in a power plant and also support Low-Voltage Ride-Through (LVRT) capability during voltage sag fault. Since the voltage sag period is short, a fast dynamic performance along with a soft behavior of the controller is the most important issue in the LVRT duration. Recently, some methods like Proportional Resonant (PR) controllers, have been presented to control the single phase PV systems in LVRT mode. However, these methods have had uncertainties in respect their contribution in LVRT mode. In PR controllers, a fast dynamic response can be obtained by tuning the gains of PR controllers for a high bandwidth, but typically the phase margin is decreased. Therefore, the design of PR controllers needs a tradeoff between dynamic response and stability. To fill in this gap, this paper presents a fast and robust current controller based on a Model-Predictive Control (MPC) for single-phase PV inverters in other to deal with the LVRT operation. In order to confirm the effectiveness of the proposed controller, results of the proposed controller are compared with the classical PR controller. They are also implemented in a 1 kW single-phase transformerless HERIC (Highly Efficient and Reliable Inverter Concept) inverter.