In　this　paper,　we　study　the　Landsberg　curvature　of　a　Finsler　metric　via　conformal　navigation　problem.　We　show　that　the　Landsberg　curvature　of　F　is　proportional　to　its　Cartan　torsion　where　F　is　the　Finsler　metric　produced　from　a　Landsberg　metric　and　its　closed　vector　field　in　terms　of　the　conformal　navigation　problem　generalizing　results　previously　known　in　the　cases　when　F　is　a　Randers　metric　or　the　Funk　metric　on　a　strongly　convex　domain.　We　also　prove　that　the　Killing　navigation　problem　has　the　Landsberg　curvature　preserving　property　for　a　closed　vector　field.