This paper presents a dynamic analysis and the control design for a three-phase three-wire unity power factor rectifier with a LCL filter. The control algorithm is based on the sliding mode control techniques that provides good tracking performance and robustness with respect to parameter variations, and a PI controller to regulate the DC voltage. The sliding control design uses a decoupling matrix to solve the algebraic constraint on the grid currents. The control law has been tested in numerical simulations with satisfactory results. © 2014 IEEE.