A mechanical alloy (MA) produced by grinding in a ball mill of mixture of powders of Mg + 10 wt.% TiH2 + 10 wt.% Fe in argon atmosphere and eight cycles of its hydrogenation/dehydrogenation are carried out. Thermal stability and hydrogen sorption properties of mechanical alloy have been studied employing thermodesorption spectroscopy at hydrogen pressure of 0.1 MPa. Activation energy of process of hydrogen desorption from hydride phase of MA has been determined. Hydrogen capacity of MA is equal to 4.9 wt.%, the temperature of start of hydrogen desorption from it-310 degrees C. The influence of long-term exposure to the air on hydrogen-sorption properties is studied. It has been established that the produced MA has kinetics characteristics, thermal stability, and hydrogen capacity similar to those of Mg + 10 wt.% Ti mechanical alloy composite produced by the reactive mechanical alloying method.