We investigate the thermal convection in a fluid layer overlying an anisotropic porous medium with Oldroyd-B fluids in the paper. The linear stability analysis and the Chebyshev pseudo-spectral method are used to obtain the numerical results. We found that the neutral curves are bimodal at some depth ratios. The proper values of the permeability ratio and the thermal diffusivity ratio are found to stabilize the stationary convection and the oscillatory convection. Furthermore, the variation of permeability ratio does not affect the bimodal nature of the neutral curves. In addition, the increase in the stress relaxation time has an unstable effect on the oscillatory convection, but the strain retardation time has the opposite effect.