By considering the fluctuation of grand potential Ω around equilibrium with respect to small density fluctuations δρα(r), the phase instability of binary Gaussian core model has been investigated and characterized. The spinodal of this model is obtained by using its direct correlation functions calculated in the hypernetted chain(HNC) approximation. Our analysis shows that this phase transition is predominately demixing. The results in HNC approximation have been compared with that in the random phase approximation.