Densification and grain growth of (Ca1-x, Mgx)Zr4(PO4)6 (CMZP; where x=0.0, 0.1, and 0.4) ceramics at the intermediate stage of sintering have been investigated. A lattice-diffusion model proposed by Coble with tetrakaidecahedron as a grain shape was employed and appears to be applicable to the sintering of CMZP. The apparent diffusion coefficient of the CMZP ceramics for x=0.0 is lower by approximately three and one orders of magnitude than for x=0.1 and x=0.4, respectively. The grain growth in CMZP at the intermediate stage of sintering follows a third-power kinetics, i.e. n=3. A modified expression using the lattice-diffusion model associated with grain-growth kinetics has been derived which makes the microstructures of CMZP controllable.