Convective seepage flow plays a key role not only in naturally forming mineral deposits and oil reservoirs, but also in the carbon-dioxide sequestration in fluid-saturated rocks. This paper presents a steady-state numerical solver, which is based on the finite element method (FEM) and progressive asymptotic approach procedure (PAAP), to solve steady-state convective seepage flow problems in fluid-saturated heterogeneous rocks. Although this kind of flow problem is commonly solved by using transient-state numerical solvers, the use of the proposed steady-state numerical solver, which is the main characteristic of this study, can have certain advantages. After the proposed steady-state numerical solver is verified by a benchmark testing problem, for which analytical solutions are available for comparison, it is further applied to simulate steady-state convective seepage flow in the Australia North West Shelf basin, which is composed of naturally-formed heterogeneous porous rocks. Through the simulated numerical results, it can be found that: (1) compared with the analytical solutions of the benchmark testing problem, the use of the steady-state numerical solver can produce correct and accurate numerical simulation results for dealing with convective seepage flow problems in fluid-saturated heterogeneous rocks. (2) The main advantage of using the steady-state numerical solver is to avoid the need of considering initial conditions of the problem, which are commonly difficult to be determined because the convective seepage flow within the upper crust is a past event in geology. (3) In the Australia North West Shelf basin, the convective seepage flow and temperature distribution patterns depend strongly on both the permeability contrast of the faults and the basin geometry (including the layer structures and fault locations) in the computational model.