In this work, the polymer melt filling process is simulated by using a coupled finite volume and level-set based immersed boundary (LS-IB) method. Firstly, based on a shape level set (LS) function to represent the mold boundary, a LS-IB method is developed to model the complex mold walls. Then the non-isothermal melt filling process is simulated based on non-Newtonian viscoelastic equations with differ-ent Reynolds numbers in a circular cavity with a solid core, and the effects of Reynolds number on the flow patterns of polymer melt are presented and compared with each other. And then for a true polymer melt with a small Reynolds number that varies with melt viscosity, the moving interface, the temperature distributions and the molecular deformation are shown and analyzed in detail. At last, as a commonly used application case, a socket cavity with seven inserts is investigated. The corresponding physical quantities, such as the melt velocity, molecular deformation, normal stresses, first normal stress differ-ence, temperature distributions and frozen layer are analyzed and discussed. The results could provide some predictions and guidance for the polymer processing industry.