Lid-driven cavity flows have been widely investigated and accurate results have been achieved as benchmarks for testing the accuracy of computational methods. This paper investigates sensitivity of a mesh refinement method against the accuracy of numerical solutions of the 2-D steady incompressible lid-driven flow from a collocated finite volume method. The sensitivity analysis is shown by comparing the coordinates of centres of primary and secondary vortices located by the mesh refinement method with the corresponding benchmark results. The accuracy of the numerical solutions is shown by comparing the profiles of horizontal and vertical components of velocity fields with the corresponding benchmarks and the streamlines. The sensitivity analysis shows that the mesh refinement method provides accurate coordinates of primary and secondary vortices depending on the accuracy of the numerical solutions. The adaptive mesh refinement method considered can be applied to incompressible fluid or steady state fluid flows or mass and heat transfer.