We investigate the stability of a gravitationally collapsing iron core against nonspherical perturbation. The gravitationally collapsing iron core is approximated by a similarity solution for a dynamically collapsing polytropic gas sphere. We find that the similarity solution is unstable against nonspherical perturbations. The perturbation grows in proportion to (t - t(0))(-sigma) while the central density increases in proportion to (t - t(0))(-2). The growth rate is sigma = 1/3 + l(gamma - 4/3), where gamma and l denote the polytropic index and the parameter l of the spherical harmonics, Y-l(m)(theta, phi), respectively. The growing perturbation is dominated by vortex motion. Thus, it excites global convection during the collapse and may contribute to material mixing in a Type II supernova.