The detailed stereodynamics of the reaction Li+HF(v=0–3) with different collision energy and in different vibration-excited state has been carried out by using the quasi-classical trajectory (QCT) method based on a new potential energy surface constructed by Aguado and Pariagua (Aguado and Paniagua J. Chem. Phys., Vol. 119, No. 19, 2003). The correlated k-j', k-k'-j' angular distributions and the polarization-dependent differential cross sections (PDDCSs) are discussed in detail. The results indicate that the collision energy has more impact on the P(θr) distributions describing the k-j' correlation than the vibration excitation. The distributions of P(φr) describing the k-k'-j' correlation, as well as the polarization-dependent generalized differential cross-sections, are sensitive to the vibration excitation. Meanwhile, the collision energy also has more influence on them.