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Abstract The physical properties of Mg-carbonate at high temperature and pressure are crucial for understanding the deep carbon cycle. Here, we use first-principles calculations to study the physical properties of MgCO3-C2/m and Mg2CO4-P21/c under high pressure. The research shows that the structure and equation of state of MgCO3-C2/m are in good agreement with the experimental results, and the phase transition pressure of Mg2CO4 from pnma to P21/c structure is 44.66 GPa. By comparing the elastic properties, seismic properties and anisotropy of MgCO3-C2/m and Mg2CO4-P21/c, it is found that the elastic modulus and sound velocity of Mg2CO4-P21/c are smaller than those of MgCO3-C2/m, while the anisotropy is larger than that of MgCO3-C2/m. These results indicate that Mg2CO4-P21/c exists in the deep mantle and may be the main reason why carbonate cannot be detected. The minimum thermal conductivity of MgCO3-C2/m and Mg2CO4-P21/c is the largest in the [010] direction and the smallest in the [001] direction. The thermodynamic properties of MgCO3-C2/m and Mg2CO4-P21/c are predicted using the quasi-harmonic approximation (QHA) method.