In this paper, creeping motion of a viscoelastic drop falling through a Newtonian fluid is investigated experimentally and analytically. A polymeric solution of 0.08 % xanthan gum in 80:20 glycerol/water and silicon oil is implemented as the viscoelastic drop and the bulk viscous fluids, respectively. The shape and motion of falling drops are visualized using a high speed camera. The perturbation technique is employed for both interior and exterior flows, and Deborah and capillary numbers are considered as perturbation parameters up to second order. The product of Deborah and capillary numbers is also used as a perturbation parameter to apply the boundary condition on the deformation on the interface of viscoelastic drop and viscous media. We used the Giesekus nonlinear constitutive equation for the drop phase for the first time. It is shown that the obtained analytical solution has better agreement with experimental observations than the previous analytical studies.