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Purpose The aim of this study is to numerically simulate the density-driven convection in heterogeneous porous media associated with anisotropic permeability field, which is important to the safe and stable long term CO2 storage in laminar saline aquifers. Design/methodology/approach The study uses compact finite difference and the pseudospectral method to solve Darcy’s law. Findings The presence of heterogeneous anisotropy may result in non-monotonic trend of the breakthrough time and quantity of CO2 dissolved in the porous medium, which are important to the CO2 underground storage. Originality/value The manuscript numerically study the convective phenomena of mixture contained CO2 and brine. The phenomena are important to the process of CO2 enhanced oil recovery. Interesting qualitative patterns and quantitative trends are revealed in the manuscript.