Different metal ions doped hydroxyapatite (HAp) nanoparticles were prepared by the sol–gel method. The phase analysis and the average surface roughness are determined using powder.X-ray diffraction (XRD) and atomic force microscopy (AFM), respectively. The synthesized dual-ions doped hydroxyapatite nanoparticles exhibit a stable HAp structure without any impurity peaks. The higher roughness (Ra) value of 65.839 nm and the lower roughness (Ra) value of 4.5276 nm were obtained for Magnesium-Zinc HAp (Mg-ZnHAp) and Copper-Zinc HAp (Cu-Zn-HAp) samples, respectively. We found the hardness value increased with the addition of dual dopant ions in HAp. The decrease in hardness of the (Mg-ZnHAp) sample is found to be due to a decrease in the density of dopant ions in HAp. The modification in the dielectric properties of dual-ions doped HAp by varying the temperature as a function of frequency is analyzed. Temperature-dependent dielectric studies unveiled the non-Debye-type relaxation behaviour in the synthesized samples. The dielectric values as a function of frequency show the deviations in peaks are due to polarization with respect to different temperatures.