This paper performed a linear stability analysis for investigating the onset of oscillatory convection of a viscoelastic fluid in an open-top porous medium heated from below.The modified Darcy's law was used to describe the flow of the viscoelastic fluid in porous media and isobaric boundary conditions were introduced to describe the open features The relaxation time and retardation time were introduced to describe the viscoelastic behaviors.Four different combinations of and were selected to calculate the critical Rayleigh numbers corresponding to the onset of thermal convection.The results reveal that the increase of the relaxation time may make it easier to destabilize the flow

leading to an earlier onset of thermal convection.In contrast

the increase of retardation time tends to stabilize the flow and postpone the onset of convection.The flow mode is only related with retardation time.The pattern of temperature disturbance is influenced by the geometric scale of the porous media and the viscoelastic parameters.