Locating accurate centres of vortices is one of the accuracy measures for computational methods in fluid flow and the lid-driven cavity flows are widely used as benchmarks. This paper analyses the accuracy of an adaptive mesh refinement method using 2D steady incompressible lid-driven cavity flows. The adaptive mesh refinement method performs mesh refinement based on the numerical solutions of Navier–Stokes equations solved by Navier2D, a vertex centred Finite Volume code that uses the median dual mesh to form the Control Volumes (CVs) about each vertex. The accuracy of the refined meshes is demonstrated by the centres of vortices obtained in the benchmarks being contained in the twice refined cells. The adaptive mesh refinement method investigated in this paper is proposed based on the qualitative theory of differential equations. Theoretically infinite refinements can be performed on an initial mesh. Practically we can stop the process of refinement based on tolerance conditions. The method can be applied to find accurate numerical solutions of any mathematical models containing the continuity equation for incompressible fluid or steady-state fluid flow.