The motion of inertial particles suspended in a turbulent channel flow is numerically simulated by means of a new dispersion model based on accurate modelling of the directional dependence of the fluid Lagrangian time scales. The continuum phase is described by a non-linear low-Reynolds k-ε model, whereas the dispersed phase motion is predicted by a Lagrangian stochastic method aimed at taking the non-homogeneity and the anisotropy of turbulence into account. The fluid Lagrangian time scales in each direction are assessed following a recent proposal supported by channel flow DNS computations. The integral time scales of the fluid seen by the particles are then estimated in taking the inertia and crossing trajectory effects into account. The numerical predictions (particle and fluid statistical quantities) obtained using this model are compared to previously available formulations of the Lagrangian time scales and to recent experimental data from the literature about the motion of small glass beads in a turbulent vertical channel flow. The new Lagrangian time scale formulation is found to yield very satisfactory results compared to the measurements.