The effect of a plane wall on the orbiting motion of a freely suspended prolate or oblate spheroidal particle in simple shear flow is described by numerical simulation. The particle translational and angular velocities are computed directly by solving an integral equation of the second kind using a spectral boundary-element method for Stokes flow. The presence of the wall modifies the Jeffery orbits executed by the particle director, and causes the particle centre to perform a lateral and transverse periodic motion deviating from the straight longitudinal path. The effect of the wall is moderate for prolate particles and most significant for oblate particles. In the second case, the complete orbiting motion is suppressed when the particle is sufficiently close to the wall, and the particle director precesses around an axis that is tilted with respect to the vorticity and direction of the simple shear flow, revealing that a neutrally stable steady orientation is established when the particle is in contact with the wall.