The control-volume finite element method (CVFEM) has been used widely to simulate the mold filling process in polymer processing because it is more user friendly and more robust than the conventional finite element or finite difference methods. However; using lower order interpolation functions in CVFEM may result in significant numerical errors. This is especially true for convection-diffusion problems with a changeable source term as in reactive liquid composite molding (LCM). In this study, an Eulerian-Lagrangian approach is proposed where art Eulerian coordinate system is used to solve the velocity field, while the chemical species balance and the energy balance are based on a Lagrangian coordinate system. This approach is used to simulate the non-isothermal LCM process.