It is found that a single icosahedral quasicrystalline phase is formed as a primary precipitation phase in the melt-spun Zr70Pd30 binary glassy alloy with a two-stage crystallization process. The onset temperature of the transformation from the amorphous to the icosahedral phase is 701 K at the heating rate of 0.67 K s-1. The size of the icosahedral particles lies in the diameter range below 10 nm and the particles are distributed homogeneously. The second-stage crystallization reaction results in the formation of a Zr2Pd phase through a single exothermic reaction. The formation of the nanoscale icosahedral phase indicates the possibility that icosahedral short-range order exists in the Zr-Pd binary glassy state. Comparison with the thermal stability of an icosahedral phase in the Zr-Ni-Pd system shows that the icosahedral phase is stabilized by the addition of Ni. The stabilization is due to the restraint of the long-range rearrangement of the constitutional elements resulting from the strong chemical affinity between Zr and Ni.