The thermal stability and crystallization kinetics of the Mg65Cu25Y10 and Mg65Cu25-xY10Bx (numbers indicate at.%, x = 1-10) amorphous alloys are examined and compared in terms of non-isothermal and isothermal differential scanning calorimetry measurements. It is demonstrated that, with the minor addition of 1-5 at.% B, the incubation time for crystallization is prolonged and the activation energy is increased, suggesting an improvement of the thermal stability. Nevertheless, the overall nucleation and growth characteristics of the parent and B-additive alloys are similar. The minor B element appears to impose resistance to the crystallization of the major Mg2Cu phase, possibly by blocking the path of Mg and Cu diffusion. With further addition of B upto 10 at.%, secondary crystallization phases such as MgB4 or YB would be induced and thus lower the thermal stability.