In this contribution we present the predator-prey model with Allee effect and hawk and dove tactics in fighting over caught prey implemented as fast strategy evolution dynamics. We extend the work of Auger, Parra, Morand and Sánchez (2002) using the prey population embodying Allee efect and analogously to this work we get two connected submodels with polymorphic and monomorphic predator population. We get much richer dynamics, in each submodel we find local bifurcations (saddle-node and Hopf caused by Allee effect) and a global bifurcation of limit cycles caused by the strategy evolution that is not possible in any of the submodels.