The　dynamical　behaviors　of　a　Leslie　type　predator-prey　system　are　explored　when　the　functional　response　is　increasing　for　both　predator　and　prey.　Qualitative　and　quantitative　analysis　methods　based　on　stability　theory,　bifurcation　theory　and　numerical　simulation　are　adopted.　It　is　showed　that　the　system　is　dissipative　and　permanent,　and　its　solutions　are　bounded.　Global　stability　of　the　unique　positive　equilibrium　is　investigated　by　constructing　Dulac　function　and　applying　Poincare-Bendixson　theorem.　The　bifurcation　behaviors　are　further　explored　and　the　number　of　limit　cycles　is　determined.　By　calculating　the　first　Lyapunov　number　and　the　first　two　focus　values,　it　is　proved　that　the　positive　equilibrium　is　not　a　center　but　a　weak　focus　of　multiplicity　at　most　two,　so　the　system　undergoes　Hopf　bifurcation　and　Bautin　bifurcation.　The　normal　form　of　Bautin　bifurcation　is　also　obtained　by　introducing　the　complex　system.　Moreover,　numerical　simulations　are　run　to　demonstrate　the　validity　of　theoretical　results.