Novel Mg-Zr-A (A=Na, Li and K) hydrides have been synthesized by the gigapascal hydrogen pressure method. Their crystal structures were analyzed based on synchrotron X-ray diffraction (XRD) patterns. In the Mg-Zr-H system, the Mg-Zr hydride with FCC structure was formed under 8 GPa and 873 K. In the case of Mg-Zr-Li and Mg-Zr-K systems, the quaternary hydrides were formed and these retained the same crystal structure, FCC structure, up to x = 1.0 While in the Mg-Zr-Na system, the quaternary hydrides were formed and these retained the FCC structure, up to x = 0.3. With the addition of 0.5 NaH, a hydride with the Ca7Ge type structure was formed instead of the FCC structure. The Mg-Zr-(Li, Na, K) hydrides can reversibly absorb and desorb hydrogen. The hydrogen desorption temperatures of those hydrides decrease with the increasing ionic radius of the alkali metal.