The transient axisymmetric extrusion swelling flow of a high viscosity fluid was simulated using FVM method with VOF technique in the present paper. The rheological property of the fluid was characterized by Cross model on the basis of the shear property of IUPAC-LDPE melt. The calculation was verified by comparing against the computational swelling of Newtonian fluid reported previously. The simulated swell ratio of 1.085 was obtained using Cross model and VOF method at the shear rate of 10 s^-1, which is higher than the result of 1.04 calculated by the steady FEM numerical method. The possible causes were analyzed.