This paper is concerned with the numerical analyses of an S-shaped duct for the inter-channel between compressor spools. For the compactness and lightweight of an engine, the length of the S-shaped duct is desired to be minimized. Shortening the S-shaped duct, however, flow separation is likely to occur. Numerical investigation using a three-dimensional Navier-Stokes flow solver was performed to determine the availability of the minimization of an S-shaped duct. Computations were performed introducing the experimental data as the inlet flow condition of the OGV in determining the minimum length of the S-shaped duct. Also, the leaning effect of the OGV which assists the flow to turn radially inward was studied adopting mixing-plane method to consider the rotor/OGV interaction.