The inter-turbine transition duct (ITD) of a gas turbine engine has significant potential for engine weight reduction and/or aerodynamic performance improvement. This potential arises because very little is understood of the flow behavior in the duct in relation to the hub and casing shapes and the flow entering the duct (e.g., swirl angle, turbulence intensity, periodic unsteadiness and blade tip vortices from upstream HP turbine blade rows). In this study, the flow development in an ITD with different inlet swirl distributions was investigated experimentally and numerically. The current paper, which is the first part of a two-part paper, presents the investigations of the influences of the casing swirl variations on the flow physics in the ITD. The results show a fair agreement between the predicted and experimental data. The radial pressure gradient at the first bend of ITD drives the low momentum hub boundary layer and wake flow radially, which results in a pair of hub counter-rotating vortices. Furthermore, the radially moving low momentum wake flow feeds into the casing region and causes 3D casing boundary layer. At the second bend, the reversed radial pressure gradient together with the 3D casing boundary layer generates a pair of casing counter-rotating vortices. Due to the local adverse pressure gradient, 3D boundary layer separation occurs on both the casing and hub at the second bend and the exit of the ITD, respectively. The casing 3D separation enhances the 3D features of the casing boundary layer as well as the existing casing counter-rotating vortices. With increasing casing swirl angle, the casing 3D boundary layer separation is delayed and the casing counter-rotating vortices are weakened. On the other hand, although the hub swirls are kept constant, the hub counter-rotating vortices get stronger with the increasing inlet swirl gradient. The total pressure coefficients within the ITD are significantly redistributed by the casing and hub counter-rotating vortices.