We consider the effect of a supernova (SN) explosion in a very massive binary that is expected to form in a portion of Population III stars with the mass higher than 100M$_solar$. In a Population III binary system, a more massive star can result in the formation of a black hole (BH) and a surrounding accretion disc. Such BH accretion could be a significant source of the cosmic reionization in the early Universe. However, a less massive companion star evolves belatedly and eventually undergoes a SN explosion, so that the accretion disc around a BH might be blown off in a lifetime of companion star. In this paper, we explore the dynamical impact of a SN explosion on an accretion disc around a massive BH, and elucidate whether the BH accretion disc is totally demolished or not. For the purpose, we perform three- dimensional hydrodynamic simulations of a very massive binary system, where we assume a BH of 10$^3$M$_solar$ that results from a direct collapse of a very massive star and a companion star of 100M$_solar$ that undergoes a SN explosion. We calculate the remaining mass of a BH accretion disc as a function of time. As a result, it is found that a significant portion of gas disc can survive through three-dimensional geometrical effects even after the SN explosion of a companion star. Even if the SN explosion energy is higher by two orders of magnitude than the binding energy of gas disc, about a half of disc can be left over. The results imply that the Population III BH accretion disc can be a long-lived luminous source, and therefore could be an important ionizing source in the early Universe.