The rheology of a dilute viscoelastic suspension of spheroids subjected to unconfined shear flow is studied by numerical simulations. To highlight the effect of the suspending fluid rheology, two viscoelastic constitutive equations, i.e., the Giesekus and the Phan-Thien-Tanner models, have been selected. Simulations are performed for a spheroid with two aspect ratios (4 and 8). The spherical particle case is also investigated for comparison. The Deborah number D e is varied between 0 and 4. The particle contribution to the viscosity is weakly affected by the particle shape and orientation. In contrast, spheroids oriented with major axis out of the vorticity direction significantly reduce the particle contribution to the first and second normal stress difference. The maximum reduction is found in the flow-alignment regime. Simulations of the transient dynamics of the suspension show that the initial distribution of the particle orientation has a remarkable influence on the evolution of the stress coefficients. The time needed to obtain steady-state rheological properties is at least one order of magnitude higher than the fluid characteristic time.