In this paper, we consider one of open problems in Finsler geometry which presented by Chen-Shen on Douglas surfaces. First, we prove that a Finsler surface has isotropic Berwald curvature if and only if it is of isotropic mean Berwald and relatively isotropic Landsberg curvature. Then we solve the open problem and show that on Douglas surfaces, a Finsler metric has isotropic mean Berwald curvature if and only if it has relatively isotropic Landsberg curvature
