In　this　work,　we　propose　and　study　a　two　species　Lotka-Volterra　competition　model,　where　the　first　species　experiences　the　mate-finding　Allee　effect　caused　by　the　second　species.　First,　we　study　the　presence　and　stability　of　all　conceivable　positive　equilibria　and　boundary　equilibria　of　this　system.　Next,　by　utilizing　the　Sotomayor　theorem,　we　demonstrate　that,　given　appropriate　parameter　circumstances,　both　a　saddle-node　bifurcation　and　a　transcritical　bifurcation　exist.　Finally,　numerical　simulations　were　carried　out　to　validate　our　theoretical　results　further.　We　found　that　under　certain　conditions,　the　system　appears　to　be　bistable　when　the　trait-mediated　indirect　effect　is　low.　However,　when　the　trait-mediated　indirect　effect　is　too　high,　the　bistability　of　the　system　disappears,　and　the　first　species　eventually　tends　to　extinction.