In this paper, a circuit topology composed of a single-phase bridgeless rectifier and a LC series branch in parallel connection is proposed, with the aim at adding power quality management capability to the traditional single-phase bridgeless rectifier. A corresponding control strategy using the third harmonic injection pulse width modulation (THIPWM) technique is also presented. The proposed circuit topology with the corresponding control strategy enable the traditional single-phase bridgeless rectifier to operate under leading, lagging or unity power factor with near-sinusoidal current in the point of common coupling of the grid. The principle of the proposed topology is discussed in detail at first, and then based on the computation to the reactive power injected by a inductive-resistive load connected at PCC, the capability of the single-phase bridgeless rectifier for reactive power compensation (RPC) is studied, and the relationship between this capability and the amount of active power transferred to the load is analyzed as well. Finally, simulation results are given to validate the feasibility of the proposed circuit topology and the correctness of theoretical analysis.