We carried out accurate quantum wave packet as well as quasi-classical trajectory (QCT) calculations for H + CaCl (ν_i = 0, j_i = 0) reaction occurring on an adiabatic ground state using the recent ab initio potential energy surface to obtain the quantum and QCT reaction probabilities for several partial waves (J = 0, 10, and 20) as well as state resolved QCT integral and differential cross sections. The complete list of vibrational energy levels supported by the intermediate HCaCl complex is also obtained using the Lanczos algorithm. The QCT reaction probabilities show excellent agreement with the quantum ones except for the failure in reproducing the highly oscillatory resonance structure. Despite the fact that the reaction is exothermic and the existence of a barrier that is energetically lower than the bottom of the reactant valley, the reaction probability for J = 0 shows threshold-like behavior and the reactivity all through the energies is very low (<0.1). The dynamical features at two different energy regions (<0.35 eV and >0.35 eV) are found to be different drastically from each other. The analyses of these results suggest that the reaction is governed by one of the two different types of reaction mechanism, one is the direct mechanism at the high energy region and the other is the indirect mechanism at the low energy region by which the reaction proceeds through the long-lived intermediate complex followed by a statistical dissociation into asymptotic channels.