In this paper, the method of density functional theory (DFT) and density functional perturbation theory (DFPT) based on the first principles are used to calculate the crystal structures, phonon spectra and density of modes for ZnCo3(OH)6Cl2 and ZnNi3(OH)6Cl2. Both of them have hexagonal crystal structures. Also, the symmetries and frequencies and thermodynamic properties are analyzed and compared. No imaginary frequencies are presented in the phonon spectra obtained from the theoretical calculation, which indicated that the crystal structures are stable; the results of density of modes showed the contribution of different kinds of atoms. The symmetries and frequencies of Raman active vibration modes are determined, and we also compared them with quantum spin liquid materials ZnCu3(OH)6Cl2, the results showed that the main positions of Raman peak are close. Finally, the thermodynamic properties calculated and analyzed agree with the laws of physics.