Ba+HF reaction is an interesting example whether for the experiment or theoretical research. But no potential energy surface for this reaction emerges for a long time because of the difficulty of the exact ab initio caused by the large mass number of the Ba atom. The first quasiclassical trajectory calculation for the exothermic reaction Ba+HF (v,J) → BaF(v′,J′)+H is carried out based on a constructed extended-LEPS PES. The calculated BaF product state distributions agree closely with experiment for both Ba+HF(v=0) and Ba+HF(v=1) . The reaction mechanism is described as following two pathways, abstraction and insertion, and the small increment of the barrier height along with the attacking deviation from the linear direction (Ba-F-H) is the main cause of this competition. Low collision energy favors abstraction whereas high vibration excitation leads to insertion.