Secondary flow losses can be as high as 30~50% of the total aerodynamic losses for a turbo-machinery blade or stator row. These are important part for improving a turbine efficiency. Therefore, many studies have been performed to decrease the secondary flow losses. The present study deals with the chamfered leading-edge at a generic wing-body junction to decrease the horseshoe vortex, one of factors to generate the secondary flow losses, and investigates the vortex generation and the characteristics of the horseshoe vortex with the chamfered height, and depth of the chamfer by using $FLUENT^{TM}$. It was found that the total pressure loss for the best case can be decreased about 1.55% compare to the baseline case.