In　this　paper,　a　two-species　competitive　model　with　Michaelis–Menten　type　harvesting　in　the　first　species　is　studied.　We　have　made　a　detailed　mathematical　analysis　of　the　model　to　describe　some　important　results　that　may　be　produced　by　the　interaction　of　biological　resources.　The　permanence,　stability,　and　bifurcation　(saddle-node　bifurcation　and　transcritical　bifurcation)　of　the　model　are　investigated.　The　results　show　that　with　the　change　of　parameters,　two　species　could　eventually　coexist,　become　extinct　or　one　species　will　be　driven　to　extinction　and　the　other　species　will　coexist.　Moreover,　by　constructing　the　Lyapunov　function,　sufficient　conditions　to　ensure　the　global　asymptotic　stability　of　the　positive　equilibrium　are　given.　Our　study　shows　that　compared　with　linear　harvesting,　nonlinear　harvesting　can　exhibit　more　complex　dynamic　behavior.　Numerical　simulations　are　presented　to　illustrate　the　theoretical　results.　©　2020,　The　Author(s).