The present paper deals with the current control of a voltage source inverter connected to the grid through an LCL filter. It proposes model suitable for analysis and control that accounts for the switching behaviour of the converter. Based on this improved model, a model predictive control scheme is proposed, in order to provide a high bandwidth response, making it very suitable for applications such as active filtering. The control scheme is extended with an observer in order to reduce the number of required sensors and to eliminate noise. The effectiveness of the proposed scheme is demonstrated by experiments.