The dynamics and kinetics of the Li + H2(+) reaction have been studied by means of quantum mechanical (QM) real wave packet, wave packet with flux operator, and quasiclassical trajectory (QCT) calculations on the ab initio potential energy surface of Martinazzo et al. [J. Chem. Phys., 2003, 119, 21]. Total initial state-selected reaction probabilities for the title reaction have been calculated for total angular momentum J = 0 at collision energies from threshold up to 1 eV. Wave packet reaction probabilities at selected values of the total angular momentum up to J = 60 are obtained using the centrifugal sudden approximation (CSA). Integral cross sections and rate constants have been calculated from the wave packet reactions probabilities by means of a refined J-shifting method and the separable rotation approximation in combination with the CSA for J > 0. The calculated rate constants as function of temperature show an Arrhenius type behavior. The QM results are found to be in overall good agreement with the corresponding QCT data.