Three-dimensional turbulent flow and heat transfer in an internally finned tube with a blocked core-tube have been numerically studied by the realizable k - turbulence model with the wall-function method. The numerical method is validated by comparing the calculated results with experimental data. The range of ratio of blocked core-tube outside diameter to outer-tube inside diameter (d(0)/D-i) is from 0.25 to 0.75. The computational results demonstrated that there exists an optimal ratio of (d(0)/D-i) under both identical mass flow rate and identical pressure drop. The optimal ratio of (d(0)/D-i), which is reduced with the increase of mass flow rate, is approximately 0.5 to 0.625 at given mass flow rate for both constant wall temperature and uniform wall heat flux. The optimal ratio of (d(0)/D-i) at a given pressure drop is from 0.44 to 0.50, which is also slightly reduced with the increase of pressure drop. Furthermore, the optimal ratio of (d(0)/D-i) is not sensitive to the number of cross-section wavy fins of an internally longitudinal finned tube, in the range of a fin wave number of 15-25.