Rare earth elements have excellent catalytic effects on improving hydrogen storage properties of the Mg2Ni-based alloys. This study used a small amount of Y to substitute Mg partially in Mg2Ni0.9Co0.1 and characterized and discussed the effects of Y on the solidification and de-/hydrogenation behaviors. The Mg2−xYxNi0.9Co0.1 (x = 0, 0.2, 0.3, and 0.4) hydrogen storage alloys were prepared using a metallurgy method. The phase composition of the alloys was studied using X-ray diffraction (XRD). Additionally, their microstructure and chemical composition were studied using scanning electron microscopy and energy-dispersive X-ray spectroscopy, respectively. The hydrogen absorption and desorption properties of the alloys were studied using pressure-composition isotherms and differential scanning calorimetric (DSC) measurements. The structure of the as-cast Mg2Ni0.9Co0.1 alloy was composed of the peritectic Mg2Ni, eutectic Mg–Mg2Ni, and a small amount of pre-precipitated Mg–Ni–Co ternary phases, and was converted into the Mg2NiH4, Mg2Ni0.9Co0.1H4, and MgH2 phases after hydrogen absorption. Furthermore, the XRD patterns of the alloys showed the MgYNi4 phase and a trace amount of the Y2O3 phase along with the Mg and Mg2Ni phases after the addition of Y. After hydrogen absorption, the phase of the alloys was composed of the Mg2NiH4, MgH2, MgYNi4, YH3, Y2O3, and Mg2NiH0.3 phases. With the increase of Y addition, the area ratios of the peritectic Mg2Ni matrix phase in the Mg2−xYxNi0.9Co0.1 (x = 0, 0.2, 0.3, and 0.4) alloys gradually decreased until they disappeared. However, the eutectic structure gradually increased, and the microstructures of the alloys were obviously refined. The addition of Y improves the activation performance of the alloys. The alloy only needed one cycle of de-/hydrogenation to complete the activation for x = 0.4. The DSC curves showed that the initial dehydrogenation temperatures of Mg2Ni0.9Co0.1 and Mg1.8Y0.2Ni0.9Co0.1 were 200 and 156 °C, respectively. The desorption activation energies of the hydrides of the Mg2Ni0.9Co0.1 and Mg1.8Y0.2Ni0.9Co0.1 alloys calculated using the Kissinger method were 94.7 and 56.5 kJ/mol, respectively. Moreover, the addition of Y reduced the initial desorption temperature of the alloys and improved their kinetic properties.