An angled labyrinth seal is used for the diaphragm-packing-ring seal design of steam turbine due to its leakage reduction characteristic. CFD analysis using FLUENT has been performed to predict leakage and determine an optimum slanted angle which yields the best leakage reduction. Results show that the optimum value of slanted angle is $-30^{circ}$ independent of number of labyrinth teeth, inlet pressure, and tooth height to pitch ratio. 3D CFD analysis has been performed for predicting leakage of the angled labyrinth seal. Comparing with the result of 2D CFD analysis, 3D CFD analysis shows 1.4% smaller.