This thesis proposes a new bidirectional three-phase AC-DC power converter using matrix converter and Z-source inverter topologies. Advantages of the AC-DC matrix converter are the inherently controllable power factor, the tight DC voltage regulation, the wide bandwidth with quick response to load variation, the single-stage buck-voltage AC-to-DC power conversion; advantages of the z-source inverter are the increased reliability by allowing the shoot-through between upper and lower power switches of one inverter leg, insensitivity to DC bus voltage due to the extra freedom of controlling DC-link voltage. The proposed Matrix-Z-source converter (MZC) marries up both advantages of AC-DC matrix converter and Z-source inverter. It can achieve voltage-boost DC-AC inversion capable of variable voltage variable frequency (VVVF) AC output; it can achieve voltage-buck AC-DC rectification capable of inherent control over AC current phase angle and DC output regulation with a (VVVF) AC source supply. Both foresaid performance in DC-AC inversion and AC-DC rectification can be implemented in a simple open-loop control manner. Three constraints of VSI, in the bidirectional AC-DC power conversion, are the peak AC voltages are always less than DC-link voltage, closed-loop control has to be employed when DC regulation and/or AC current phase angle control are required, and AC voltage is sensitive to the variation of the DC-link voltage in DC-AC inversion. The voltage-boost inversion and/or voltage-buck rectification of MZC overcomes the first constraint; thus MZC enables the AC machine voltage increased higher than DC-link voltage hence advantages of running AC machine at relatively high voltages are enabled. The direct DC voltage regulation and inherent AC-current-phase-angle control of MZC overcomes the second constraint in an open-loop manner; hence a simplified system design is obtained with sufficient room for the further improvement by closed-loop control schemes. The extra freedom in controlling DC-link voltage of MZC overcomes the third constraint hence a DC source voltage adaptable inverter is obtained. This thesis focuses on the study of the feasibility of the proposed MZC through theoretical analysis and experimental verification. At first, the proposed MZC is conceptually constructed by examining the quadrant operation of AC-DC matrix converter and Z-source inverter. After the examination of the operating principles of both AC-DC matrix converter and Z-source inverter, the configuration of MZC is then proposed. The MZC has two operating modes: DC-AC inversion and AC-DC rectification. Circuit analysis for both operating modes shows that the new topology does not impose critical conflict in circuit design or extra restriction in parameterization. On the contrary, one version of the proposed MZC can make full advantage of Z-source network components in both operating modes, i.e. a pair of Z-source inductor and capacitor can be used as low-pass filter in AC-DC rectification. The modulation strategy, average modeling of system, and features of critical variables for circuit design of the proposed MZC were examined for each operating mode. Simulations of the proposed MZC and its experimental verification have been presented. Analytical models of conduction and switching losses of the power-switch network in different operating mode have shown that the losses in the MZC compare favorably with conventional VSI for a range of power factor and modulation indices.