We present two-dimensional numerical simulations of core-collapse supernova including multi-energy neutrino radiative transfer. We aim to examine the influence of the equation of state (EOS) for the dense nuclear matter. We employ four sets of EOSs, namely, those by Lattimer and Swesty (LS) and Shen et al., which became standard EOSs in the core-collapse supernova community. We reconfirm that not every EOS produces an explosion in spherical symmetry, which is consistent with previous works. In two-dimensional simulations, we find that the structure of the accretion flow is significantly different between LS EOS and Shen EOS, inducing an even qualitatively different evolution of the shock wave, namely, the LS EOS leads to shock propagation beyond 2000 km from the center, while the Shen EOS shows only oscillations within 500 km. The possible origins of the difference are discussed.