This paper presents the topology, analysis, and control implementation of a new single-phase flexible power quality conditioner (FPQC), which can be used for handling voltage- and current-related power quality (PQ) problems. Different from other PQ-compensating devices, the FPQC can work under two compensating modes, i.e., parallel-connection mode (PCM) and series-connection mode (SCM). When the source voltage is unpolluted, the FPQC is working under the PCM so that the load harmonic current and reactive power can be compensated. When the source voltage is polluted, the FPQC is switched to the SCM to mitigate the impact caused by the polluted voltage. In this way, a desired voltage can be maintained at the load side to protect the critical load. The mode switching between PCM and SCM is realized by two relays. To ensure fast dynamics response and smooth transient operation, the model predictive control method is applied to regulate the developed FPQC. Both the simulation platform and laboratorial prototype are built to validate the effectiveness of the system. The simulation and experimental results are presented and discussed.