Trajectories of inertial spheroidal particles moving in a shear flow near a solid wall are calculated numerically from the Stokes flow equations by computing the hydrodynamic forces and torques acting on the particles. Near the wall these interactions cause coupling between the particle's rotational and translational motions. Due to this coupling an inertial spheroid is shown to move along an oscillatory trajectory, while simultaneously drifting towards the wall. This phenomenon occurs in the absence of gravity as a combined effect of three factors: particle non-spherical shape, its inertia and particle-wall hydrodynamic interactions. This drift is absent for inertialess spheroids, and also for inertial spherical particles which move along flow streamlines. The drift velocity is calculated for various particle aspect ratios y and relaxation times τ. An approximate solution, valid for small particle inertia is developed, which allows the contribution of various terms to the drift velocity to be elucidated. It was found that the maximum value of the drift velocity prevails for N(γ)γ2τs ∼ 4, where s is the shear rate and N(γ) is a decreasing function of γ, related to the particle-wall hydrodynamic interactions. In the limiting cases of large and small inertia and also of very long and thin spheroids, the drift vanishes. Possible applications of the results are discussed in the context of transport of micrometre particles in microgravity conditions. It is shown that the model used is applicable for analysis of the deposition of aerosol particles with sizes above 10 μm inhaled in the human respiratory tract in the absence of gravity.