Density-driven convection, which can accelerate the dissolution rate of carbon dioxide (CO2) in resident brine, is critical for the long-term fate of the injected CO2 permanence and security of CO2 geological storage. Visualization experiments and pressure-volume-temperature (PVT) testing were conducted to investigate the influence from gravitational convection. For investigate gravitational instabilities and convective diffusion, we designed a Hele-Shaw cell rated to 70 MPa and Rayleigh number of 346 to conduct visualization experiments with the micro-schlieren technique. The average diffusion coefficient and time-dependent values were measured in the PVT experiments. We also calculated the convection parameters, including Rayleigh number and critical onset time, with a series of PVT testing at the temperature ranging 293.15-423.15 K and pressure ranging 14-24 MPa by using the constant-pressure method. Through visualization experiments, we observed convective currents triggered by the density gradient in the gas-liquid interface, which noticeably enhanced the CO2 dissolution rate. The PVT testing confirmed that the diffusion coefficient increased sharply under the influence of the gravitational convection at the early stage and then decreased toward the average diffusion coefficient with time. The PVT testing also demonstrated the Rayleigh number increasing with temperature or pressure increasing under the reservoir conditions. The gravitational convection will be more likely to occur and more rapid with a greater pressure or higher temperature.