Abstract Numerical simulation of steam-flooding thermal heavy oil recovery is studied in this paper. Although the traditional full implicit scheme has high stability, it needs to calculate the huge sparse matrix and the computation cost is super expensive; so it cannot meet the needs of practical oil industry production. In this paper, sequential implicit scheme is applied to numerical computation of steam-flooding thermal heavy oil recovery. A quasi-one-dimension numerical example is tested to verify the validity and high efficiency of the proposed method against using traditional fully implicit scheme.