Fast ignition is an epoch-making scheme for inertial fusion energy. In this scheme, the formation of high-density core plasma is one of the key issues which must be solved, because the implosion dynamics of the fast ignition target, which is non-spherical with a conical target, is quite different from that of the conventional central ignition target. Some previous works showed the possibility of formation of a high-density core. However, the effects of hydrodynamic instability were not discussed in those works. In this paper, we simulate the whole implosion dynamics of a perturbed non-spherical target, and the effect of radiation transport instability is estimated using the two-dimensional integrated implosion (radiation hydrodynamics) code PINOCO. In the result, we have found that the hydrodynamic instabily has less of an effect on the formation of high-density core plasma in the cone-guided implosion, in comparision with the spherical implosion.