Hydroxyapatite is known to have excellent catalytic properties for ethanol conversion and lactic acid conversion, and their properties are influenced by the elemental composition, such as Ca/P ratio and sodium content. However, few reports have been examined for the surface acid–base nature of hydroxyapatites containing sodium ions. We prepared nanocrystalline hydroxyapatite (Ca-HAP) catalysts with various Ca/P ratios and sodium contents by the hydrothermal method. The adsorption and desorption experiments using NH3 and CO2 molecules and the catalytic reactions for 2-propenol conversion revealed that the surface acid–base natures changed continuously with the bulk Ca/P ratios. Furthermore, the new catalytic properties of hydroxyapatite were exhibited for 1,6-hexanediol conversion. The non-stoichiometric Ca-HAP(1.54) catalyst with sodium ions of 2.3 wt% and a Ca/P molar ratio of 1.54 gave a high 5-hexen-1-ol yield of 68%. In contrast, the Ca-HAP(1.72) catalyst, with a Ca/P molar ratio of 1.72, gave a high cyclopentanemethanol yield of 42%. Both yields were the highest ever reported in the relevant literature. It was shown that hydroxyapatite also has excellent catalytic properties for alkanediol conversion because the surface acid–base properties can be continuously controlled by the elemental compositions, such as bulk Ca/P ratios and sodium contents.