This paper proposes an open-circuit fault-tolerant design for the cascaded H-Bridge rectifier incorporating reactive power compensation. If one or two switching devices of the H-bridge modules are fault, the drive signals of the faulty H-bridge modules will be artificially redistributed into the bridgeless mode (including the boost bridgeless mode, the symmetric boost bridgeless mode, the totem-pole bridgeless mode and the symmetry totem-pole bridgeless mode) and cooperate with the normally operated H-bridge modules. In this case, the faulty cascaded H-bridge rectifier is not only able to achieve active power transmission, but also can still provide part of reactive power compensation when injecting reactive power from the power grid. Nonetheless, the reactive power that it can supply will be limited, due to the unidirectional characteristics of the bridgeless mode for the faulty modules. Therefore, a method for calculating its adjustable power factor angle range is also presented, which provides the basis for the faulty modules switching to the bridgeless mode. Then, a control strategy of the cascaded H-bridge rectifier incorporating reactive power compensation under the faulty condition and normal operation is presented. Finally, an experimental platform with a single-phase cascaded H-bridge rectifier containing three cells is given to verify the proposed theories.