With an eye toward application to the theory of core-collapse supernovae, we performed a global linear analysis on the stability of spherically symmetric accretion flows through a standing shock wave onto a proto neutron star. We solved the equations for linear perturbations numerically, and obtained the eigen frequencies and eigen functions. The results show that the non-radial instabilities are induced, probably via the advection-acoustic cycles, for relatively low neutrino luminosities, e.g. ∼2-7×1052ergs/s for M=1.0M⊙/s. For still larger luminosities, more than about 7×1052ergs/s for the same accretion rate, non-oscillatory modes become unstable. These non-radial modes were identified as convection.