Model configurations of turbine blade trailing-edge internal cooling passage with staggered elliptic pin-fins in streamwise and spanwise are adopted for numerical investigation using computational fluid dynamics (CFD). Grid refinement study is performed at first to identify a baseline mesh, followed by validation study of passage total pressure loss, which gives 2% and 4% discrepancies respectively for two chosen configurations in comparison with experimental measurements. Further investigations are focused on evaluation of wall heat transfer coefficient (HTC) of both pin-fin and end walls, and it is found that CFD predicted pin-fin wall HTC are generally in good agreement with test data for the streamwise staggered elliptic pin-fins, but not the spanwise staggered elliptic pin-fins in which some discrepancies occur. CFD predicted end wall HTC have shown reasonable good agreement for the first three rows, but discrepancies seen in downstream rows are around a factor of 2-3. A ratio of averaged pin-fin and end walls HTC is estimated 1.3-1.5, close to that from a circular pin-fin configuration that has 1.8-2.1. Further study should focus on improving end wall HTC predictions, probably through a conjugate heat transfer model.