The crystal growth of calcite at a low temperature range was carried out by the hydrothermal method using amorphous calcium carbonate which has excellent solubility in water. Amorphous calcium carbonate was prepared by the wet chemical reaction of a stoichiometric mixture of $CaCl_2;and;Na_2CO_3$. An important factor was the reaction temperature and time taken in preparation of the amorphous calcium carbonate. From the solubility results calculated by the weight loss method, $NH_4NO_3$ solutions were found to be the most promising solvents to grow calcite single crystals. The hydrothermal conditions for high growth rates of calcite single crystals were as follows: starting material: amorphous calcium carbonate, solvent: 0.01 m $NH_4NO_3$, temperature: $180^{circ}C$, duration: 30 days. And properties of calcite single crystals were follows: dislocation density: $10^6{sim}10cm^{-2}$, UV-visible transmittance: about 80% from 190 to 400 nm and birefringence: $0.17{sim}0.18$. Also, it can be known from the FT-IR results that the absorption peak by injection of $HCO_3^-;and;OH^-$ ions was not shown.