Sequestering carbon dioxide ( \(\hbox {CO}_2\) ) in deep-ocean sediments is deemed as a promising approach to reducing carbon emissions. Under the low-temperature high-pressure condition of deep-ocean sediments, there may exist hydrate formation zone (HFZ) where solid \(\hbox {CO}_2\) hydrate forms and negative buoyancy zone (NBZ) where \(\hbox {CO}_2\) is denser than water. Both of the HFZ and the NBZ suppress the upward movement of the \(\hbox {CO}_2\) plume; therefore, permanent storage was proposed in the deep-ocean sediment even if there is no low-permeability caprock on the top of the reservoir. However, in virtue of numerical simulations on \(\hbox {CO}_2\) injection over a wide range of deep-ocean sediment conditions, we find that neither the HFZ, the NBZ nor the combination of the HFZ and NBZ makes sufficient condition for permanent \(\hbox {CO}_2\) storage in the deep-ocean sediment, and we cannot evaluate the \(\hbox {CO}_2\) storage security simply based on the existence of the HFZ and the NBZ. This is because (1) only a very small amount of hydrate forms in the HFZ and the formed hydrate may dissociate with continuous \(\hbox {CO}_2\) injection and (2) the negative gravitation trapping by the NBZ may fail if the permeability of the sediment is not high enough to make the negative buoyancy force effective. We also find that the NBZ may shrink because the temperature increase due to exothermic hydrate formation may significantly reduce \(\hbox {CO}_2\) density and we propose a new method to calculate the size of the NBZ. Finally, unconditional permanent \(\hbox {CO}_2\) storage may only exist in high-permeability sediments with NBZ.