The viscoelastic flow and swell behaviors of polymer melts in the profile extrusion process can significantly influence the performance and dimension of the final products. In the study, the viscoelastic flow pattern of a commercial low density polyethylene (LDPE) extruded through out of the hollow profiled extrusion die is investigated by means of finite element simulation. The mathematical model of three-dimensional viscoelastic flow and swell of polymer melts is established with a differential Phan-Thien and Tanner (PTT) constitutive model. A penalty method is employed to solve the non-linear problem with a decoupled algorithm. The computation stability is improved by using the discrete elastic-viscous split stress (DEVSS) algorithm with the inconsistent streamline-upwind (SU) scheme. A streamface-streamline method is introduced to adjust the swelling free surface of the extrudate. The essential viscoelastic flow characteristics of LDPE flowing through out of the hollow profile extrusion die is investigated based on the proposed numerical scheme. Both the redistribution of flow velocity and the release of stress are found to be the reasons for the swell phenomenon.