In this paper, the time-dependent wave-packet method is used to study the three-dimensional dynamical properties of the H+Li2 reactive system on its ground state potential energy surface. The reaction probabilities for J=0 with different vibrational quantum numbers v=0, 1, 2, 3 and for v=0 with different total rotational quantum numbers, integral cross sections and rate constants are calculated for collision energies in a range between 0 and 0.4 eV. The features of the reaction probabilities and reaction threshold energy are analyzed. The results show that the vibrational excitation has a certain inhibitory effect on the reaction process and the reaction threshold energy increases with the increase of J. These phenomena are associated with the type of the exothermic reaction of the reactive system. The influence of the collision energy on the integral cross sections and the effect of the temperature on reaction rate constants are also investigated.