In order to increase the integrity of the wellbore which is used to prevent the leakage of supercritical $CO_2$, it is necessary to develop a concrete that is strongly resistant to carbonation. In an environment where the concentration of $CO_2$ is exceptionally high, $Ca^{2+}$ ion concentration in pore solution of Portland cement concrete will drop significantly due to the rapid consumption of calcium hydroxide, which decreases the stability of the calcium silicate hydrate. In this research, calcium phosphates were used to modify Portland cement system in order to produce hydroxyapatite, a hydration product that is strongly resistant to carbonation under such an environment. According to the experimental results, calcium phosphates reacted with Portland cement to form hydroxyapatite. The formation of hydroxyapatite was verified using X-ray diffraction analyses with selective extraction techniques. When using dicalcium phosphate dihydrate and tricalcium phosphate, the 28-day compressive strength was lower than that of plain cement paste. However, the specimen with monocalcium phosphate monohydrate showed equivalent strength to that of plain cement paste.