A new numerical method for simulation of vis-coelastic fluid flow is proposed, based on a previously developed Lagrangian-Eulerian. The viscoelastic constitutive equation is solved in Lagrangian nodes with a backwards-tracking procedure and the fluid momentum and continuity equations are discretized with the finite volume method on an adaptive octree grid. Two-fluid flow is modeled with the Volume of Fluid method. The new method improves both the robust-ness and computational efficiency in comparison to the original method. A validation is performed for a viscoelastic planar Poiseuille flow, as well as for simulation of industrial scale adhesive application on an automotive part. The results are in good agreement with available analytic and experimental data. The results also demonstrate the robustness of the numerical framework for simulating complex, industrial scale viscoelastic flows.