Path　following　is　a　fundamental　problem　in　skid-steered　mobile　robots　(SSMR).　In　this　study,　a　Lyapunov　stable　curved　path　following　controller　was　designed　to　generate　the　steering　control　command　for　an　SSMR.　In　contrast　to　the　existing　path　following　controller　design　methods,　where　the　complete　dynamic　model　of　the　robot　is　considered　or　not,　the　steering　dynamic　characteristics　approximated　by　a　first-order　model　are　considered　in　this　study.　Together　with　the　kinematic　model,　a　steering　control　law　for　following　a　curved　path　is　designed　by　using　the　backstepping　technique　and　Lyapunov　stability　theory.　The　proposed　method　was　verified　on　a　real　SSMR　platform　to　realize　following　the　straight-line,　square,　and　circular　paths.　Compared　with　the　steering　control　law　that　does　not　consider　the　steering　dynamics,　the　proposed　method　can　make　the　robot　converge　to　the　predefined　path　faster　with　a　smaller　error　overshoot.