This　paper　is　the　first　to　propose　an　allelopathic　phytoplankton　competition　ODE　model　influenced　by　the　fear　effect　based　on　natural　biological　phenomena.　It　is　shown　that　the　interplay　of　this　fear　effect　and　the　allelopathic　term　cause　rich　dynamics　in　the　proposed　competition　model,　such　as　global　stability,　transcritical　bifurcation,　pitchfork　bifurcation,　and　saddle-node　bifurcation.　We　also　consider　the　spatially　explicit　version　of　the　model　and　prove　analogous　results.　Numerical　simulations　verify　the　feasibility　of　the　theoretical　analysis.　The　results　demonstrate　that　the　primary　cause　of　the　extinction　of　non-toxic　species　is　the　fear　of　toxic　species　compared　to　toxins.　Allelopathy　only　affects　the　density　of　non-toxic　species.　The　discussion　guides　the　conservation　of　species　and　the　maintenance　of　biodiversity.