A three-dimensional computational code was developed for solving a time-averaged flow within a turbine blade-to-blade region using a novel time-marching method. A new concept of incorporating dissipation terms into the time derivative terms was proposed to allow the code to have the capability of handling both incompressible and compressible flows. The computational code was validated through comparisons with experiments in a turbine stator and was used to investigate the influence of secondary flow depending on different pitch-width ratios of the turbine blades. Detailed secondary flows as well as loss profiles in different sizes of root pitch-width ratio were presented. The results of this study provide useful information for evaluation of the secondary flow effects due to pitch-width ratio influence for the future turbine designs.